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2-Transitive Designs

  • Conference paper
Combinatorics

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 16))

Abstract

A great deal of work was done on 2-transitive groups during the last century and the beginning of this one. There has been a recent resurgence of interest in them for several reasons. First of all, many finite simple groups either have 2-transitive permutation representations or are closely related to groups that do. Also, recent work on finite simple groups has made the study of permutation groups more accessible. Finally, the close relationship between these groups and finite geometries has been recognized and has benefitted both group theory and geometry.

The preparation of this paper was supported in part by NSF Grant GP 37982X.

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References

  1. Aschbacher, M., On doubly transitive permutation groups of degree n Ξ 2 mod 4, Illinois J. Math., 16 (1972) 276–279.

    MathSciNet  MATH  Google Scholar 

  2. Aschbacher, M., Doubly transitive groups in which the stabilizer of two points is abelian, J. Algebra, 18 (1971) 114–136.

    Article  MathSciNet  MATH  Google Scholar 

  3. Aschbacher, M., A condition for the existence of a strongly embedded subgroup, Proc. Amer. Math. Soc., 38 (1973) 509–511.

    Article  MathSciNet  MATH  Google Scholar 

  4. Aschbacher, M., F-Sets and permutation groups, to appear.

    Google Scholar 

  5. Aschbacher, M., 2-Transitive groups whose 2-point stabilizer has 2-rank 1, to appear.

    Google Scholar 

  6. Atkinson, M.D., Doubly transitive but not doubly primitive permutation groups I, J. London Math. Soc. (2), 7 (1974) 632–634; II, ibid., to appear.

    Article  MathSciNet  MATH  Google Scholar 

  7. Bender, H., Endliche zweifache transitive Permutationsgruppen, deren Involutionen keine Fixpunkte haben, Math. Z., 104 (1968) 175–204.

    Article  MathSciNet  MATH  Google Scholar 

  8. Bender, H., Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festlasst, J. Algebra, 17 (1971) 527–554.

    Article  MathSciNet  MATH  Google Scholar 

  9. Block, R.E., Transitive groups of collineations of certain designs, Pacific J. Math., 15 (1965) 13–19.

    MathSciNet  MATH  Google Scholar 

  10. Bruen, A. &B. Levinger, A theorem on permutations of a finite field, Canad. J. Math., 25 (1973) 1060–1065.

    Article  MathSciNet  MATH  Google Scholar 

  11. Buekenhout, F., Une caractérisation des espaces affins basée sur la notion de droite, Math. Z., 111 (1969) 367–371.

    Article  MathSciNet  MATH  Google Scholar 

  12. Buekenhout, F., A characterization of affine spaces of order two as 3-designs, Math. Z., 118 (1970) 83–85.

    Article  MathSciNet  MATH  Google Scholar 

  13. Buekenhout, F., An axiomatic of inversive spaces, J. Combinatorial Theory A, 11 (1971) 208–212.

    Article  MathSciNet  MATH  Google Scholar 

  14. Buekenhout, F., On 2-designs whose group of automorphisms is transitive on the ordered pairs of intersecting lines, J. London Math. Soc., 5 (1972) 663–672.

    Article  MathSciNet  MATH  Google Scholar 

  15. Buekenhout, F., Transitive groups whose involutions fix one or three points, J. Algebra, 23. (1972) 438–451.

    Article  MathSciNet  MATH  Google Scholar 

  16. Buekenhout, F., Doubly transitive groups in which the maximum number of fixed points of involutions is four, Arch. Math. (Basel), 23 (1972) 362–369.

    MathSciNet  MATH  Google Scholar 

  17. Buekenhout, F. & R. Deherder, Espaces linéaires finis à plans isomorphes,. Bull. Soc. Math. Belg., 23 (1971) 348–359.

    MathSciNet  MATH  Google Scholar 

  18. Burnside, W., Theory of groups of finite order, Dover, New York, 1955.

    MATH  Google Scholar 

  19. Cameron, P.J., Structure of suborbits in some primitive permutation groups, thesis, Oxford Univ., 1971.

    Google Scholar 

  20. Cameron, P.J., Permutation groups with multiply transitive suborbits I, Proc. London Math. Soc. (3), 25 (1972) 427–440; II, Bull. London Math. Soc., to appear.

    Article  MathSciNet  MATH  Google Scholar 

  21. Cameron, P.J., Primitive groups with most suborbits doubly transitive, Geometriae Dedicata, 1 (1973) 434–446.

    Article  MathSciNet  MATH  Google Scholar 

  22. Cameron, P.J., Extending symmetric designs, J. Combinatorial Theory A, 14 (1973) 215–220.

    Article  MATH  Google Scholar 

  23. Cameron, P.J., Biplanes, Math. Z., 131 (1973) 85–101.

    Article  MathSciNet  MATH  Google Scholar 

  24. Cameron, P.J., On groups with several doubly transitive permutation representations, Math. z., 128 (1972) 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  25. Cameron, P.J., Near-regularity conditions for designs, Geometriae Dedicata, 2 (1973) 213–224.

    Article  MathSciNet  MATH  Google Scholar 

  26. Cameron, P.J., Permutation groups with multiply-transitive suborbits II, to appear.

    Google Scholar 

  27. Cameron, P.J., Locally symmetric designs, to appear.

    Google Scholar 

  28. Cameron, P.J., On groups of degree n and n-1, and highly symmetric edge colourings, to appear.

    Google Scholar 

  29. Cameron, P.J., Characterizations of some Steiner systems, parallelisms, and biplanes, to appear.

    Google Scholar 

  30. Cameron, P.J. & J.J. Seidel, Quadratic forms over GF(2), Indag. Math., 35 (1973) 1–8.

    MathSciNet  Google Scholar 

  31. Carlitz, L., A theorem on permutations of a finite field, Proc. Amer. Math. Soc., 11 (1960) 456–459.

    Article  MathSciNet  MATH  Google Scholar 

  32. Carmichael, R.D., Introduction to the theory of groups of finite order, Dover, New York, 1956.

    Google Scholar 

  33. Cassels, J.W.S., Factorization of polynomials in several variables, in: Proc. 15th Scandinavian Congress 1968, Lecture Notes in Mathematics 118, Springer-Verlag, Berlin, 1970.

    Google Scholar 

  34. Conway, J.H., A group of order 8, 315, 553, 613, 086, 720, 000, Bull. London Math. Soc., 1 (1969) 79–88.

    Article  MathSciNet  MATH  Google Scholar 

  35. Conway, J.H., Three lectures on exceptional groups, in: Finite simple groups, Academic Press, New York, 1971, pp.215–247.

    Google Scholar 

  36. Curtis, C.W., W.M. Kantor & G.M. Seitz, The 2-transitive permutation representations of the finite Chevalley groups, to appear.

    Google Scholar 

  37. Czerwinski, T., Collineation groups containing no Baer involutions, Proc. Internat. Conference on Projective Planes, Washington State Univ. Press, Pullman, 1973.

    Google Scholar 

  38. Dembowski, P., Verallgemeinerungen von Transitivitätsklassen endlichen projektiver Ebenen, Math. Z., 69 (1958) 59–89.

    Article  MathSciNet  MATH  Google Scholar 

  39. Dembowski, P., Die Nichtexistenz von transitiven Erweiterungen der endlichen affinen Gruppen, J. Reine Angew. Math., 220 (1965) 37–44.

    Article  MathSciNet  MATH  Google Scholar 

  40. Dembowski, P., Finite geometries, Ergebnisse der Mathematik 44, Springer-Verlag, Berlin etc., 1968.

    Google Scholar 

  41. Dembowski, P. & A. Wagner, Some characterizations of finite projective spaces, Arch. Math. (Basel), 11 (1960) 465–469.

    MathSciNet  MATH  Google Scholar 

  42. Dickson, L.E., Linear groups, Dover, New York, 1955.

    Google Scholar 

  43. Doyen, J. & X. Hubaut, Finite regular locally projective spaces, Math. Z., 119 (1971) 83–88.

    Article  MathSciNet  MATH  Google Scholar 

  44. Feit, W., Automorphisms of symmetric balanced incomplete block designs, Math. Z., 118 (1970) 40–49.

    Article  MathSciNet  MATH  Google Scholar 

  45. Feit, W., On symmetric balanced incomplete block designs with doubly transitive automorphism groups, J. Combinatorial Theory A, 14 (1973) 221–247.

    Article  MathSciNet  MATH  Google Scholar 

  46. Feit, W. & J.G. Thompson, Solvability of groups of odd order, Pacific J. Math., 13 (1963) 771–1029.

    MathSciNet  Google Scholar 

  47. Fischer, B., Eine Kennzeichnung der symmetrischen Gruppen von Grade 6 und 7, Math. Z., 95 (1967) 288–298.

    Article  MathSciNet  MATH  Google Scholar 

  48. Fischer, B., Finite groups generated by 3-transpositions, I, Invent. Math., 13 (1971) 232–246.

    Article  MATH  Google Scholar 

  49. Fried, M., On the diophantine equation f(y)-x = 0, Acta Arith., 19 (1971) 79–87.

    MathSciNet  MATH  Google Scholar 

  50. Fried, M., The field of definition of function fields and a problem in the reducibility of polynomials in two variables, Illinois J. Math., 17 (1973) 128–146.

    MathSciNet  MATH  Google Scholar 

  51. Fried, M., On Hilbert’s irreducibility theorem, J. Number Theory, to appear.

    Google Scholar 

  52. Fried, M. & D.J. Lewis, Solution spaces to diophantine problems, Bull. Amer. Math. Soc., to appear.

    Google Scholar 

  53. Glauberman, G., Central elements in core-free groups, J. Algebra, 4 (1966) 403–420.

    Article  MathSciNet  MATH  Google Scholar 

  54. Goethals, J.M. & J.J. Seidel, Strongly regular graphs derived from combinatorial designs, Canad. J. Math., 22 (1970) 597–614.

    MathSciNet  MATH  Google Scholar 

  55. Hall, J.I., Steiner triple systems with geometric minimally generated subsystems, to appear.

    Google Scholar 

  56. Hall, Jr., M., A survey of difference sets, Proc. Amer. Math. Soc., 7 (1956) 975–986.

    Article  MathSciNet  Google Scholar 

  57. Hall, Jr., M., The theory of groups, MacMillan, New York, 1959.

    MATH  Google Scholar 

  58. Hall, Jr., M., Automorphisms of Steiner triple systems, IBM J. Res. Develop., 4 (1960) 460–472. (Also in Proc. Symp. Pure Math. 6 (1962) 47–66).

    Article  MathSciNet  MATH  Google Scholar 

  59. Hall, Jr., M., Note on the Mathieu group M 12 , Arch. Math. (Basel), 13 (1962) 334–340.

    MathSciNet  MATH  Google Scholar 

  60. Hall, Jr., M., Group theory and block designs, in: Proc. Internat. Conf. Theory of Groups, Gordon & Breach , New York, 1967, pp.115–144.

    Google Scholar 

  61. Hall, Jr., M., Combinatorial theory, Blaisdell, Waltham, Mass., 1967.

    Google Scholar 

  62. Hall, Jr., M., Symmetric block designs with λ = 2, in: Combinatorial mathematics and its applications, Univ. of North Carolina Press, 1969, pp.175–186.

    Google Scholar 

  63. Harada, K., On some doubly transitive groups, J. Algebra, 17 (1971) 437–450.

    Article  MathSciNet  MATH  Google Scholar 

  64. Hering, C., Zweifach transitive Permutationsgruppen, in denen zwei die maximale Anzahl von Fixpunkten von Involutionen ist, Math, z., 104 (1968) 150–174.

    Article  MathSciNet  MATH  Google Scholar 

  65. Hering, C., On linear groups which contain an irreducible subgroup of prime order, in: Proc. Internat. Conf. Projective Planes, Washington State Univ. Press, Pullman, 1973.

    Google Scholar 

  66. Hering, C., W.M. Kantor & G.M. Seitz, Finite groups having a split BN-pair of rank 1, J. Algebra, 20 (1972) 435–475.

    Article  MathSciNet  MATH  Google Scholar 

  67. Hering, F., Über die Kollineationsgruppen einiger Hadamard-Matrizen, unpublished manuscript.

    Google Scholar 

  68. Higman, D.G., Flag transitive collineation groups of finite projective spaces, Illinois J. Math., 6 (1962) 434–446.

    MathSciNet  MATH  Google Scholar 

  69. Higman, D.G., Finite permutation groups of rank 3, Math. Z., 86 (1964) 145–156.

    Article  MathSciNet  MATH  Google Scholar 

  70. Higman, D.G., Characterization of families of rank 3 permutation groups by the subdegrees II, Arch. Math. (Basel), 21 (1970) 353–361.

    MathSciNet  MATH  Google Scholar 

  71. Higman, D.G., Remark on Shult’s graph extension theorem, in: Finite groups ’72, T. Gagen, M.P. Hale & E.E. Shult (eds.), North-Holland Publ. Coy., Amsterdam, 1973, pp. 80–83.

    Google Scholar 

  72. Hlgman, D.G. & C.C. Sims, A simple group of order 44,352,000, Math. Z., 105 (1968) 110–113.

    Article  MathSciNet  Google Scholar 

  73. Higman, G., On the simple group of D.G. Higman and C.C. Sims, Illinois J. Math., 13 (1969) 74–84.

    MathSciNet  MATH  Google Scholar 

  74. Hill, R., Rank 3 permutation groups with a regular normal subgroup, thesis, Univ. of Warwick, 1971.

    Google Scholar 

  75. Hughes, D.R., On t-designs and groups, Amer. J. Math., 87 (1965) 761–778.

    Article  MathSciNet  MATH  Google Scholar 

  76. Hughes, D.R., Extensions of designs and groups: Projective, symplectic, and certain affine groups, Math. Z., 89 (1965) 199–205.

    Article  MathSciNet  MATH  Google Scholar 

  77. Huppert, B., Zweifach transitive, auflösbare Permutationsgruppen, Math. Z., 68 (1957) 126–150.

    Article  MathSciNet  MATH  Google Scholar 

  78. Hussain, Q.M., Impossibility of the symmetrical incomplete block design with λ=2, k=7, Sankhya, 7 (1946) 317–322.

    MathSciNet  Google Scholar 

  79. Hussain, Q.M., Symmetrical incomplete block designs with λ = 2, k = 8 or 9, Bull. Calcutta Math. Soc., 37 (1945) 115–123.

    MathSciNet  Google Scholar 

  80. Ito, N., Über die Gruppen PSL n (q), die eine Untergruppe von Primzahlindex enthalten, Acta Sci. Math. (Szeged), 21 (1960) 206–217.

    MathSciNet  MATH  Google Scholar 

  81. Ito, N., On a class of doubly, but not triply transitive permutation groups, Arch. Math. (Basel), 18 (1967) 564–570.

    MathSciNet  MATH  Google Scholar 

  82. Ito, N., On permutation groups of prime degree p which contain (at least) two classes of conjugate subgroups of index p, Rend. Sem. Mat. Padova, 38 (1967) 287–292.

    Google Scholar 

  83. Ito, N., On permutation groups of prime degree p which contain at least two classes of conjugate subgroups of index p, II, Nagoya Math. J., 37 (1970) 201–208.

    MathSciNet  MATH  Google Scholar 

  84. Ito, N., A theorem on Jordan groups, in: Theory of finite groups, Benjamin, New York, 1969, pp.47–48.

    Google Scholar 

  85. Ito, N., Tight 4-designs, to appear.

    Google Scholar 

  86. Ito, N., On the Wielandt number of transitive permutation groups of prime degree, to appear.

    Google Scholar 

  87. Ito, N. & W.M. Kantor, 2-Transitive symmetric designs with k = 2p, Notices Amer. Math. Soc., 16 (1969) 774.

    Google Scholar 

  88. Jordan, C., Théorèmes sur les groupes primitifs, J. Math. Pures Appl., 16 (1871) 383–408.

    Google Scholar 

  89. Jordan, C., Oeuvres, J. Dieudonné (ed.), Gauthier-Villars, Paris, 1961.

    Google Scholar 

  90. Jordan, C., Traité des substitutions, (new edition), Gauthier-Villars, Paris, 1957.

    MATH  Google Scholar 

  91. Kantor, W.M., Automorphism groups of designs, Math. Z., 109 (1969) 246–252.

    Article  MathSciNet  MATH  Google Scholar 

  92. Kantor, W.M., Characterizations of finite projective and affine spaces, Canad. J. Math., 21 (1969) 64–75.

    Article  MathSciNet  MATH  Google Scholar 

  93. Kantor, W.M., 2-Transitive symmetric designs, Trans. Amer. Math. Soc., 146 (1969) 1–28.

    MathSciNet  MATH  Google Scholar 

  94. Kantor, W.M., Automorphisms of Hadamard matrices, J. Combinatorial Theory, 6 (1969) 279–281.

    Article  MathSciNet  MATH  Google Scholar 

  95. Kantor, W.M., Jordan groups, J. Algebra, 12 (1969) 471–493.

    Article  MathSciNet  MATH  Google Scholar 

  96. Kantor, W.M., Elations of designs, Canad. J. Math., 22 (1970) 897–904.

    Article  MathSciNet  MATH  Google Scholar 

  97. Kantor, W.M., On a class of Jordan groups, Math. Z., 118 (1970) 58–68.

    Article  MathSciNet  MATH  Google Scholar 

  98. Kantor, W.M., Note on symmetric designs and projective spaces, Math. Z., 122 (1971) 61–62.

    Article  MathSciNet  MATH  Google Scholar 

  99. Kantor, W.M., On 2-transitive groups in which the stabilizer of two points fixes additional points, J. London Math. Soc., 5 (1972) 114–122.

    Article  MathSciNet  MATH  Google Scholar 

  100. Kantor, W.M., Line-transitive collineation groups of finite projective spaces, Israel J. Math., 14 (1973) 229–235.

    Article  MathSciNet  MATH  Google Scholar 

  101. Kantor, W.M., Symplectic groups, symmetric designs, and line ovals, to appear.

    Google Scholar 

  102. Kantor, W.M., On 2-transitive collineation groups of finite projective spaces, Pacific J. Math., 48 (1973) 119–131.

    MathSciNet  MATH  Google Scholar 

  103. Kantor, W.M., Some highly geometric lattices, to appear.

    Google Scholar 

  104. Kantor, W.M., Primitive groups having transitive subgroups of smaller, prime power degree, to appear.

    Google Scholar 

  105. Kantor, W.M., Plane geometries associated with certain 2-transitive groups, to appear.

    Google Scholar 

  106. Kantor, W.M. & T.P. Mcdonough, On the maximality of PSL(d+1,q), d≥2, to appear.

    Google Scholar 

  107. Kantor, W.M., M.E. O’Nan & G.M. Seitz, 2-Transitive groups in which the stabilizer of two points is cyclic, J. Algebra, 21 (1972) 17–50.

    Article  MathSciNet  MATH  Google Scholar 

  108. Kerdock, A.M., A class of low-rate nonlinear binary codes, Information and Control, 20 (1972) 182–187.

    Article  MathSciNet  MATH  Google Scholar 

  109. King, J., Doubly transitive groups in which involutions fix one or three points, Math. Z., 111 (1969) 311–321.

    Article  MathSciNet  MATH  Google Scholar 

  110. Lüneburg, H., Über projektive Ebenen, in denen jede Fahne von einer nichttrivialen Elation invariant gelassen wird, Abh. Math. Sem. Univ. Hamburg, 29 (1965) 37–76.

    Article  MathSciNet  MATH  Google Scholar 

  111. Lüneburg, H., Die Suzukigruppen und ihre Geometrien, Lecture Notes in Mathematics 10, Springer-Verlag, Berlin etc., 1965.

    MATH  Google Scholar 

  112. Lüneburg, H., Transitive Erweiterungen endlicher Permutationsgruppen, Lecture Notes in Mathematics 84, Springer-Verlag, Berlin etc., 1969.

    MATH  Google Scholar 

  113. Mann, H.B., Addition theorems, Tracts in Pure and Applied Math. 18, Interscience, New York, 1965.

    MATH  Google Scholar 

  114. Marggraff, B., Über primitive Gruppen, welche eine transitive Gruppe geringeren Grades enthalten, thesis, Giessen, 1889.

    Google Scholar 

  115. Marggraff, B., Primitive Gruppen, welche eine transitive Gruppe geringeren Grades enthalten, Wiss. Beilage zu den Jahresberichten des Sophiengymnasiums zu Berlin, Berlin, 1895.

    Google Scholar 

  116. McConnel R., Pseudo-ordered polynomials over a finite field, Acta Arith., 8 (1963) 127–151.

    MathSciNet  MATH  Google Scholar 

  117. Mcdonough, T.P., On Jordan groups, J. London Math. Soc., 6 (1972) 73–80.

    Article  MathSciNet  MATH  Google Scholar 

  118. Mcdonough, T.P., On Jordan groups — addendum, to appear.

    Google Scholar 

  119. McLaughlin, J.E., A simple group of order 898,128,000, in: Theory of finite groups, Benjamin, New York, 1969, pp.109–111.

    Google Scholar 

  120. Nagao, H., On multiply transitive groups IV, Osaka J. Math., 2 (1965) 327–341.

    MathSciNet  MATH  Google Scholar 

  121. Neumann, P.M., Transitive permutation groups of prime degree, J. London Math. Soc., 5 (1972) 202–208.

    Article  MathSciNet  MATH  Google Scholar 

  122. Neumann, P.M., Generosity and characters of multiply transitive permutation groups, to appear.

    Google Scholar 

  123. Neumann, P.M., Transitive permutation groups of prime degree, in: Proc. Conf. Theory of Groups, Canberra 1973, Lecture Notes in Mathematics, Springer-Verlag, Berlin etc., to appear.

    Google Scholar 

  124. Neumann, P.M., Transitive permutation groups of prime degree IV, to appear.

    Google Scholar 

  125. Noda, R., Doubly transitive groups in which the maximal number of fixed points of involutions is four, Osaka Math. J., 8 (1971) 77–90.

    MathSciNet  MATH  Google Scholar 

  126. Noda, R., Steiner systems which admit block-transitive automorphism groups of small rank, Math. Z., 125 (1972) 113–121.

    Article  MathSciNet  MATH  Google Scholar 

  127. Norman, C.W., A characterization of the Mathieu group M 11 , Math. Z., 106 (1968) 162–166.

    Article  MathSciNet  MATH  Google Scholar 

  128. O’Nan, M.E., Automorphisms of unitary block designs, J. Algebra, 20 (1972) 495–511.

    Article  MathSciNet  MATH  Google Scholar 

  129. O’nan, M.E., A characterization of U 3 (q), J. Algebra, 22 (1972) 254–296.

    Article  MathSciNet  MATH  Google Scholar 

  130. O’nan, M.E., A characterization of L n (q) as a permutation group, Math. Z., 127 (1972) 301–314.

    Article  MathSciNet  MATH  Google Scholar 

  131. O’nan, M.E., The normal structure of the one-point stabilizer of a doubly-transitive group, in: Finite groups ’72, T. Gagen, M.P. Hale & E.E. Shult, (eds.), North-Holland Publ. Coy., Amsterdam, 1973, pp.119–121.

    Google Scholar 

  132. O’nan, M.E., Normal structure of the one-point stabilizer of a doubly-transitive permutation group, I, to appear.

    Google Scholar 

  133. O’Nan, M.E., Normal structure of the one-point stabilizer of a doubly-transitive permutation group, II, to appear.

    Google Scholar 

  134. O’Nan, M.E., Triply-transitive permutation groups whose two-point stabilizer is local, to appear.

    Google Scholar 

  135. O’Nan, M.E., Doubly-transitive groups of odd degree whose one point stabilizer is local, to appear.

    Google Scholar 

  136. Osborn, J.H., Finite doubly-transitive permutation groups without subgroups fixing exactly two points, thesis, Univ. of Wisconsin, 1972.

    Google Scholar 

  137. Ostrom, T.G. & A. Wagner, On projective and affine planes with transitive collineation groups, Math. Z., 71 (1959) 186–199.

    Article  MathSciNet  MATH  Google Scholar 

  138. Paley, R.E.A.C., On orthogonal matrices, J. Math. Phys., 12 (1933) 311–320.

    Google Scholar 

  139. Perin, D., On collineation groups of finite projective spaces, Math. Z., 126 (1972) 135–142.

    Article  MathSciNet  MATH  Google Scholar 

  140. Pollatsek, H., First cohomology groups of some linear groups over fields of characteristic two, Illinois J. Math., 15 (1971) 393–417.

    MathSciNet  MATH  Google Scholar 

  141. Praeger, C.E., Finite permutation groups, thesis, Oxford Univ., 1973.

    Google Scholar 

  142. Scott, L.L., A double transitivity criterion, Math. Z., 115 (1970) 7–8.

    Article  MathSciNet  MATH  Google Scholar 

  143. Seidel, J.J., A survey of two-graphs, to appear.

    Google Scholar 

  144. Shaughnessy, E.P., Codes with simple automorphism groups, Arch. Math. (Basel), 22 (1971) 459–466.

    MathSciNet  MATH  Google Scholar 

  145. Shult, E.E., On the fusion of an involution in its centralizer, to appear.

    Google Scholar 

  146. Shult, E.E., On a class of doubly transitive groups, Illinois J. Math., 16 (1972) 434–445.

    MathSciNet  MATH  Google Scholar 

  147. Shult, E.E., The graph extension theorem, Proc. Amer. Math. Soc., 33 (1972) 278–284.

    Article  MathSciNet  MATH  Google Scholar 

  148. Shult, E.E., Characterizations of certain classes of graphs, J. Combinatorial Theory B, 13 (1972) 142–167.

    Article  MathSciNet  Google Scholar 

  149. Shult, E.E., On doubly transitive groups of even degree, to appear.

    Google Scholar 

  150. Sims, C.C., On the isomorphism of two groups of order 44,352,000, in: Theory of finite groups, Benjamin, New York, 1969, pp.101–108.

    Google Scholar 

  151. Sims, C.C., Computational methods in the study of permutation groups, in: Computational problems in abstract algebra, J. Leech (ed.), Pergamon Press, London, 1970, pp. 169–183.

    Google Scholar 

  152. Smith, M.S., A combinatorial configuration associated with the Higman-Sims simple group, to appear.

    Google Scholar 

  153. Smith, M.S., On the isomorphism of two simple groups of order 44,352,000, to appear.

    Google Scholar 

  154. Sylvester, J.J., Collected mathematical papers, vol. II, Cambridge Univ. Press, 1908, pp.615–628.

    Google Scholar 

  155. Taylor, D.E., Some topics in the theory of finite groups, thesis, Oxford Univ., 1971.

    Google Scholar 

  156. Taylor, D.E., Monomial representations and strong graphs, in: Proc. First Australian Conf. Combinatorial Math., Univ. of Newcastle, 1972, pp. 197–201.

    Google Scholar 

  157. Teirlinck, L., On linear spaces in which every plane is either projective or affine, to appear.

    Google Scholar 

  158. Tits, J., Sur les systèmes de Steiner associés aux trois “grands” groupes de Mathieu, Rend. Mat. e Appl., 23 (1964) 166–184.

    MathSciNet  MATH  Google Scholar 

  159. Todd, J.A., A combinatorial problem, J. Math. Phys., 12 (1933) 321–333.

    Google Scholar 

  160. Tsuzuku, T., On doubly transitive permutation groups of degree 1+ p+ p 2 where p is a prime number, J. Algebra, 8 (1968) 143–147.

    Article  MathSciNet  MATH  Google Scholar 

  161. Veblen, O. & J.W. Young, Projective geometry I, Ginn, Boston, 1916.

    Google Scholar 

  162. Wagner, A., On collineation groups of finite projective spaces, I, Math. Z., 76 (1961) 411–426.

    Article  MathSciNet  MATH  Google Scholar 

  163. Ward, H.N., On Ree’s series of simple groups, Trans. Amer. Math. Soc., 121 (1966) 62–69.

    MathSciNet  MATH  Google Scholar 

  164. Wielandt, H., Abschätzungen für den Grad einer Permutationsgruppe von vorgeschriebenem Transitivitätsgrad, Schr. Math. Sem. Univ. Berlin, 2 (1934) 151–174.

    Google Scholar 

  165. Wielandt, H., Über den Transitivitätsgrad von Permutationsgruppen, Math. Z., 74 (1960) 297–298.

    Article  MathSciNet  MATH  Google Scholar 

  166. Wielandt, H., Finite permutation groups, Acad. Press, New York, 1964.

    MATH  Google Scholar 

  167. Wielandt, H., On automorphism groups of doubly-transitive permutation groups, in: Proc. Internat. Conf. Theory of Groups, Gordon & Breach, New York, 1967, pp.389–393.

    Google Scholar 

  168. Wilson, R.M. & D.K. Ray-Chaudhuri, Generalization of Fisher’s inequality to t-designs, Notices Amer. Math. Soc., 18 (1971) 805.

    Google Scholar 

  169. Witt, E., Die 5-faeh transitiven Gruppen von Mathieu, Abh. Math. Sem. Univ. Hamburg, 12 (1938) 256–264.

    Article  Google Scholar 

  170. Witt, E., Über Steinersche Systeme, Abh. Math. Sem. Univ. Hamburg, 12 (1938) 265–275.

    Article  Google Scholar 

  171. Zassenhaus, H., Über endliche Fastkörper, Abh. Math. Sem. Univ. Hamburg, 11 (1935) 187–220.

    Article  MATH  Google Scholar 

  172. Zassenhaus, H., Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen, Abh. Math. Sem. Univ. Hamburg, 11 (1935) 17–40.

    Article  MATH  Google Scholar 

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  1. University of Oregon, Eugene, Oregon, 97403, USA

    W. M. Kantor

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M. Hall Jr. J. H. van Lint

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© 1975 Mathematical Centre, Amsterdam

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Kantor, W.M. (1975). 2-Transitive Designs. In: Hall, M., van Lint, J.H. (eds) Combinatorics. NATO Advanced Study Institutes Series, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1826-5_19

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  • DOI: https://doi.org/10.1007/978-94-010-1826-5_19

  • Publisher Name: Springer, Dordrecht

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  • Online ISBN: 978-94-010-1826-5

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