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On partially transitive projective planes of certain Hughes types

Part of the Lecture Notes in Mathematics book series (LNM,volume 573)

Keywords

  • Normal Subgroup
  • Translation Plane
  • Transitive Group
  • Collineation Group
  • Transitive Permutation Group

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References

  1. Michael Aschbacher, "Doubly transitive groups in which the stabilizer of two points is abelian", J. Algebra 18 (1971), 114–136. MR43#2059.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Michael Aschbacher, "On doubly transitive permutation groups of degree n ≡ 2 mod 4", Illinois J. Math. 16 (1972), 276–279. MR45#8713.

    MathSciNet  MATH  Google Scholar 

  3. Helmut Bender, "Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festlässt", J. Algebra 17 (1971), 527–554. MR44#5370.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. D. Holt, "Doubly transitive groups with a solvable one point stabiliser", preprint.

    Google Scholar 

  5. D.R. Hughes, "Partial difference sets", Amer. J. Math. 78 (1956), 650–674. MR18,921.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. D.R. Hughes, "A note on some partially transitive projective planes", Proc. Amer. Math. Soc. 8 (1957), 978–981. MR19,876.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Marshall Hall, Jr., The Theory of Groups (The Macmillan Co., New York, 1959). MR21#1996.

    MATH  Google Scholar 

  8. N.L. Johnson, "A characterization of generalized Hall planes", Bull. Austral. Math. Soc. 6 (1972), 61–67. MR46#5861.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. N.L. Johnson and T.G. Ostrom, "Tangentially transitive planes of order 16", submitted.

    Google Scholar 

  10. W.M. Kantor, "2-transitive designs", Combinatorics. Part 3: Combinatorial Group Theory (Proc. Advanced Study Institute, Breuekelen, 1974, 44–97. Math. Centre Tracts, 57. Math. Centrum, Amsterdam, 1974).

    Google Scholar 

  11. Peter Lorimer, "A projective plane of order 16", J. Combinatorial Theory Ser. A 16 (1974), 334–347. MR49#3673.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. W.A. Manning, "The order of primitive groups (III)", Trans. Amer. Math. Soc. 19 (1918), 127–142. FdM46,179.

    MathSciNet  MATH  Google Scholar 

  13. Michael O'Nan, "A characterization of L n (q) as a permutation group", Math. Z. 127 (1972), 301–314. MR47#310.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Michael E. O'Nan, "Normal structure of the one-point stabilizer of a doubly-transitive permutation group, I", Trans. Amer. Math. Soc. 214 (1975), 1–42.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. A. Rahilly, "Finite generalized Hall planes and their collineation groups", PhD thesis, University of Sydney, Sydney, 1973.

    MATH  Google Scholar 

  16. Alan Rahilly, "The collineation of finite generalized Hall palnes", Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973, 589–594 (Lecture Notes in Mathematics, 372, Springer-Verlag, Berlin, Heidelberg, New York, 1974). MR50#12767.

    Google Scholar 

  17. Alan Rahilly, "Some translation planes with elations which are not translations", Combinatorial Mathematics, III. (Proc. Third Austral. Conf., Queensland, 1974, 197–209. Lecture Notes in Mathematics, 452. Springer-Verlag, Berlin, Heidelberg, New York, 1975).

    Google Scholar 

  18. Alan Rahilly, "A remarkable translation plane of order 16", submitted.

    Google Scholar 

  19. Alan Rahilly and D. Searby, "On partially transitive planes of Hughes type (6, m)", Geometriae Dedicata (to appear).

    Google Scholar 

  20. Rimhak Ree, "A family of simple groups associated with the simple Lie algebra of type (G 2)", Amer. J. Math. 83 (1961), 432–462. MR25#2123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Tosiro Tsuzuku, "On doubly transitive permutation groups of degree 1 + p + p 2 where p is a prime number", J. Algebra 8 (1968), 143–147. MR36#1527.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Helmut Wielandt, Finite Permutation Groups (translated from German by R. Bercov. Academic Press, New York, London, 1964). MR32#1252.

    MATH  Google Scholar 

  23. Ernst Witt, "Die 5-fach transitiven Gruppen von Mathieu", Abh. Math. Sem. Univ. Hamburg 12 (1938), 256–264. FdM64,963.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1977 Springer-Verlag

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Praeger, C.E., Rahilly, A. (1977). On partially transitive projective planes of certain Hughes types. In: Bryce, R.A., Cossey, J., Newman, M.F. (eds) Group Theory. Lecture Notes in Mathematics, vol 573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087815

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  • DOI: https://doi.org/10.1007/BFb0087815

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