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Semigroup Forum

, Volume 15, Issue 1, pp 1–20 | Cite as

Computers in semigroups

  • H. Jürgensen
Survey Article

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References

  1. 1.
    Биtюцкий, B.П.:Итepatиbhыe Пpoцeдypы paзлoзehия злemehtob Cиmmetpичecкиx Пoлyгpyпп. Кибернет.11, No. 5 (1975), 49–50.Google Scholar
  2. 2.
    Blackburn, J.E., H.H. Crapo, and D.A. Higgs:A catalogue of combinatorial geometries. Math. of Comp.27 (1973), 155–166 and microfiche supplement.Google Scholar
  3. 3.
    БohДapeв, B.г.:Алгоритм разложения в конечных симметрических попугруппах. Кибернет.6, No. 4 (1970), 24–28. Engl. Transl.: Cybernet.6 (1970), 388–394.Google Scholar
  4. 4.
    Bondesen, Å.:Er det en gruppetavle? Nordisk Mat. Tidskr.17 (1969), 132–136.Google Scholar
  5. 5.
    Brauer, W.:Zwei Algorithmen zur Bestimmung der maximalen Untergruppen des Transitionsmonoids eines Automaten. Seminarbericht 13, Inst. f. Theorie d. Automaten u. Schaltnetzwerke, Gesellschaft f. Math. u. Datenverarb., Bonn, 1969.Google Scholar
  6. 6.
    Brauer, W.:Zur Bestimmung der maximalen Untergruppen des Transitionsmonoids eines Automaten. EIK7 (1971), 251–260.Google Scholar
  7. 7.
    Bröck, R.:Ein Programm zur Berechnung aller Vereinigungserweiterungen zweier Halbgruppen. Diplomarbeit, Kiel, 1972.Google Scholar
  8. 8.
    Bröck, R., and H. Jürgensen:On the computation of union-extensions of finite semigroups. Acta Cybern.2 (1973), 109–113.Google Scholar
  9. 9.
    Brzozowski, J.A.:Derivatives of regular expressions. J. ACM11 (1964), 481–494.Google Scholar
  10. 10.
    Buck, R.C.:On certain decidable semigroups. Amer. Math. Monthly75 (1968), 852–856.Google Scholar
  11. 11.
    Buck, R.C.:Decidable semigroups. Bull. AMS74 (1968), 892–894.Google Scholar
  12. 12.
    Bunting, P.W., and J. van Leeuwen:Deciding associativity for partial multiplication tables of order 3. Techn. rep., Dep. Comp. Sci., Pennsylv State Univ., 1976.Google Scholar
  13. 13.
    Cannon, J.J., L.A. Dimino, G. Havas, and J.M. Watson:Implementation and analysis of the Todd-Coxeter-algorithm. Math. of Comp.27 (1973), 463–490.Google Scholar
  14. 14.
    Cannon, J.J.:Computing the ideal structure of finite semigroups. Numer. Math.18 (1971), 254–266.Google Scholar
  15. 15.
    Carman, K.S., J.C. Harden, and E.E. Posey: Common appendix of master's theses (Semigroup ideals (Carman),direct and semidirect products of semigroups (Harden),endomorphisms and translations of semigroups (Posey)). Univ. of Tennessee, 1949.Google Scholar
  16. 16.
    Clay, J.R.:The near-rings on groups of low order. Math. Zeitschr.104 (1968), 364–371.Google Scholar
  17. 17.
    Clay, J.R.:Research in near-ring theory using a digital computer. SIT10 (1970), 249–265.Google Scholar
  18. 18.
    Clifford, A.H., and G.B. Preston:The algebraic theory of semigroups,I. Providence, Rh.I., 2nd ed., 1964.Google Scholar
  19. 19.
    Cousineau, F.G., J.-F. Perrot, and J.M. Rifflet:APL programs for direct computation of a finite semigroup. In: P. Gjerløv, H.J. Helms, and J. Nielsen (eds.), APL congress 73. Amsterdam, 1973. Pp. 672-74.Google Scholar
  20. 20.
    Dade, E.C., and H. Zassenhaus:How programming difficulties can lead to theoretical advances. Proc. Symp. Appl. Math. AMS15 (1963), 87–94.Google Scholar
  21. 21.
    Dénes, J.:A bibliography on non-numerical applications of digital computers. Comp. Rev.9 (1968), 481–508.Google Scholar
  22. 22.
    Deussen, P.:On a specific similarity of finite semigroups. In R.F. Churchhouse and J.-C. Herz (eds.), Computers in mathematical research. Amsterdam, 1968. Pp. 51–55.Google Scholar
  23. 23.
    Dietze, A., and M. Schaps:Determining subgroups of a given finite index in a finitely presented group. Canad. J. Math.26 (1974), 769–782.Google Scholar
  24. 24.
    Djoković, D.Z.:On a class of semigroups. Canad. Math. Bull.12 (1969), 213–215.Google Scholar
  25. 25.
    Drazin, M.: Private communication. 1976, 1977.Google Scholar
  26. 26.
    Felsch, V.:A machine independent implementation of a collection algorithm for the multiplication of group elements. Proc. SYMSAC 76. New York, 1976. Pp. 159–166.Google Scholar
  27. 27.
    Felsch, V.:A bibliography on the use of computers in group theory and related topics:Algorithms,implementations,and applications. In preparation, to appear in SIGSAM Bull.Google Scholar
  28. 28.
    Ferber, K., and H. Jürgensen:A programme for the drawing of lattices. [46], 83–87.Google Scholar
  29. 29.
    Forsythe, G.E.:SWAG computes all 126 distinct semigroups of order 4. Bull. AMS60 (1954), 476.Google Scholar
  30. 30.
    Forsythe, G.E.:SWAC computes 126 semigroups of order 4. Proc. AMS6 (1955), 443–447.Google Scholar
  31. 31.
    ГабоВич, Е.Я.:Линейно упорядоченные полугруппы и их приложения. Уcпехи Мат. Наук31, 1 (187) (1976), 137–201. Engl. Transl.: Russian Math. Surveys31, 1 (1976), 147–216.Google Scholar
  32. 32.
    Глушков, В.М.:О полноте систем операций в злектронных вычиcлителбных машинаш. Кибернет.4, No. 2 (1968), 1–5. Engl. Transl.: Cybernet.4, No. 2 (1968), 1–4.Google Scholar
  33. 33.
    Henneman, W.:Note on “an algebraic substructure algorithm”. Math. Algorithms1, No. 2 (1966), 40.Google Scholar
  34. 34.
    Henneman, W.:The automata theorist's helper. Appendix to: R. McNaughton and S. Papert, Counterfree automata. Cambridge, Mass., 1971.Google Scholar
  35. 35.
    Hewitt, E., and H.S. Zuckerman:Finite dimensional convolution algebra. Acts. Math.93 (1955), 67–119.Google Scholar
  36. 36.
    Jürgensen, H.:Calculation with the elements of a finite group given by generators and defining relations. [46], 47–57.Google Scholar
  37. 37.
    Jürgensen, H., and P. Wick:Bestimmung der Unterhalbgruppenverbände für zwei Klassen endlicher Halbgruppen. Computing11 (1973), 337–351.Google Scholar
  38. 38.
    Jürgensen, H.:Rees-Kerne und Vereinigungserweiterungen von Halbgruppen. Kiel, 1975.Google Scholar
  39. 39.
    Jürgensen, H., and P. Wick:Die Halbgruppen der Ordnungen < 7. To appear in Semigroup Forum.Google Scholar
  40. 40.
    Jürgensen, H., I. Pallas, and P. Wick:Halbgruppenprogramme. Bericht 1/76, Inst. f. Informatik u. Prakt. Math., Univ. Kiel, 1976.Google Scholar
  41. 41.
    Jürgensen, H.:Computing the structure of finite semigroups. Lecture notes, summer school on group theor. and computation, Galway, Ireland, 1973.Google Scholar
  42. 42.
    Jürgensen, H.:Transformationendarstellungen endlicher abstrakt präsentierter Halbgruppen. Bericht 7605, Inst. f. Informatik u. Prakt. Math., Univ. Kiel, 1976. Submitted for publ.Google Scholar
  43. 43.
    Jürgensen, H.:Über das Rechnen mit den Elementen abstrakt präsentierter Halbgruppen. Bericht 7606, Inst. f. Informatik u. Prakt. Math., Univ. Kiel, 1976. Submitted for publ.Google Scholar
  44. 44.
    Kalmbacher, I.:Untersuchung des Unterhalbgruppenverbandes vollständig (O-)einfacher Halbgruppen. Diplomarbeit, Kiel, 1974.Google Scholar
  45. 45.
    Kleitman, D.J., B.R. Rothschild, and J.H. Spencer:The number of semigroups of order n. Proc. AMS55 (1976), 227–232.Google Scholar
  46. 46.
    Leech, J. (ed.):Computational problems in abstract algebra. Proc. of a conf. held at Oxford 1967. Oxford, 1970.Google Scholar
  47. 47.
    Leech, J.:Coset enumeration. [46], 21–35.Google Scholar
  48. 48.
    Leech, J.:Computer proof of relations in groups. To appear in: M. Curran (ed.), Topics in-group theory and computation.Google Scholar
  49. 49.
    Löwer, J.:Ein Zeichenprogramm für Hassediagramme partieller Ordnungen. Diplomarbeit, Kiel, 1977.Google Scholar
  50. 50.
    Марков, А.А.:Нерекуррентное кодирование. Проблемы кибернетики8 (1962), 168–186. German Transl.: Probleme d. Kybernetik8 (1965), 159–175.Google Scholar
  51. 51.
    Maurer, D.:An algebraic substructure algorithm. Math. Algorithms1, No. 1 (1966), 72–86.Google Scholar
  52. 52.
    Maurer, D.:Computer experiments in finite algebra. Comm. ACM9 (1966), 598–603, 643.Google Scholar
  53. 53.
    McAllister, K.:Implementation of the Sydney semigroup program. Dep. of Pure Math., Univ. of Sydney, 1970.Google Scholar
  54. 54.
    Motzkin, T.S., and J.L. Selfridge:Semigroups of order 5. Bull. AMS62 (1956), 14.Google Scholar
  55. 55.
    Neubüser, J.:Investigations of groups on computers. [46], 1–19.Google Scholar
  56. 56.
    Neumann, B.H.:Some remarks on semigroup presentations. Canad. J. Math.19 (1967), 1018–1026;20 (1968), 511.Google Scholar
  57. 57.
    Parrington, J.M.:A computer program for semigroups. Dep. of Math., Inst. for Advanced Stud., Austral. Nat. Univ., Canberra, 1968.Google Scholar
  58. 58.
    Pastijn, F.:A theorem concerning the restriction of the O-structure of a semigroup S to a subsemigroup of S. Math. Slovac.26 (1976), 19–22.Google Scholar
  59. 59.
    Perrot, J.-F.:Sur le calcul effectif du monoide de transitions d'un automate fini. In: W.D. Izfeldt (ed.), International computing symposium, Bonn, 1970. Bonn, 1973. Pp. 664–672.Google Scholar
  60. 60.
    Perrot, J.-F.:Contribution à l'étude des monoides syntactiques et de certains groupes associés aux automates finis. Thèse de doctorat d'état ès sciences, Univ. Paris VI, 1972.Google Scholar
  61. 61.
    Perrot, J.-F.:Calculs dans un monoide fini de transformations. Journées algorithmiques, Paris, 1975. Astérisque38-39 (1976), 203–211.Google Scholar
  62. 62.
    Perrot, J.-F.:Utilisation d'APL pour calculer des monoides finis. Proceedings of a conf. on “Utilisation des calculateurs en mathématiques pures”, Limoges, 1975. To appear in Mém. Soc. Math. France.Google Scholar
  63. 63.
    Plemmons, R.J.:Cayley tables for all semigroups of order N < 6. Auburn Univ., 1966.Google Scholar
  64. 64.
    Plemmons, R.J.:A survey of computer applications to semigroups and related structures. SIGSAM Bull. No. 12 (1969), 28–39.Google Scholar
  65. 65.
    Plemmons, R.J.:Construction and analysis of non-equivalent finite semigroups. [46], 223–228.Google Scholar
  66. 66.
    Plemmons, R.J.:There are 15973 semigroups of order 6. Math. Algorithms2 (1967), 2–17. See also:A remark the editor ... Math. Algorithms3 (1968), 23.Google Scholar
  67. 67.
    Plemmons, R.J.:On computing non-equivalent finite algebraic systems. Math. Algorithms2 (1967), 80–83.Google Scholar
  68. 68.
    Poole, A.R.:Finite ova. Ph.D. thesis, Calif. Inst. of Technol., 1935.Google Scholar
  69. 69.
    Sammet, J.E.:Software for nonnumerical mathematics. In: J.R. Rice (ed.), Mathematical software. New York, 1971. Pp. 295–330,Google Scholar
  70. 70.
    Sammet, J.E., and V. Ivinsky:Brief annotated bibliography/reference list of major items relevant to the use of computers in formal mathematics. SIGSAM Bull. No. 27 (1973), 30–31.Google Scholar
  71. 71.
    Sardines, A.A., and C.W. Patterson:A necessary and sufficient condition for the unique decomposition of coded messages. IRE Intern. Conv. Record8 (1953), 104–108.Google Scholar
  72. 72.
    Schützenberger, M.P.:Une théorie algébrique du codage. Séminaire Dubreil-Pisot (algèbre et théorie des nombres) 1955/56, No. 15.Google Scholar
  73. 73.
    Selfridge, J.L.:On finite semigroups. Ph.D. thesis, Univ. of Calif., Los Angeles, 1958.Google Scholar
  74. 74.
    Spehner, J.C.:Quelques constructions et algorithmes relatifs aux sous-monoide libre. Semigroup Forum9 (1975), 334–353.Google Scholar
  75. 75.
    Spehner, J.C.:Quelques problèmes d'extension,de conjugaison et de présentation des sous-monoides d'un monoide libre. Thèse de doctorat d'état, Univ. Paris VII, 1976.Google Scholar
  76. 76.
    Tamura, T., and T. Sakuragi:Types of semigroups of order 3. Sugaku sijo danwa, No. 5 (1952), 121–124 (in Japanese).Google Scholar
  77. 77.
    Tamura, T.:Some remarks on semigroups and all types of orders 2,3. J. of Gakugei, Tokushima Univ., (Math.)3 (1953), 1–11 and separate erratum.Google Scholar
  78. 78.
    Tamura, T.:Notes on finite semigroups and determination of semigroups of order 4. J. of Gakugei, Tokushima Univ., (Math.)5 (1954), 17–27;6 (1955), 21.Google Scholar
  79. 79.
    Tetsuya, K., T. Hashimoto, T. Akazawa, R. Shibata, T. Inui, and T. Tamura:All semigroups of order at most 5. J. of Gakugei, Tokushima Univ., (Nat. Sci. Math.)6 (1955), 19–39 and separate erratum.Google Scholar
  80. 80.
    Todd, J.A., and H.S.M. Coxeter:A practical method for enumerating cosets of a finite abstract group. Proc. Edinburgh Math. Soc. (2)5 (1937), 25–34.Google Scholar
  81. 81.
    Тодоров, К.Ж.:О подполугруппах полугруппы преобраэований конечного множества и их порядковых числах. Годишник На Софийския Унив., Фак. Мат. Мех.67, 1972/73 (1976), 327–331.Google Scholar
  82. 82.
    Totzek, J.:Bestimmung der Greenschen Relationen in einer endlichen Transformationshalbgruppe. Diplomarbeit, Kiel, 1977.Google Scholar
  83. 83.
    Verbeek, L.A.M.:Union extensions of semigroups. Trans. AMS150 (1970), 409–423.Google Scholar
  84. 84.
    Verbeek, L.A.M.:Investigating the associativity of finite groupoids by a computer program. Report, Math. Inst., Techn. Univ. Delft, 1968.Google Scholar
  85. 85.
    Walker, R.J.:Determination of division algebras with 32 elements. Proc. Symp. Appl. Math. AMS15 (1963), 83–85.Google Scholar
  86. 86.
    Wick, P.:Programme zur Berechnung des Unterhalbgruppenhalbverbandes zweier Klassen von Halbgruppen. Diplomarbeit, Kiel, 1972.Google Scholar
  87. 87.
    Wilde, C., and Sh. Raney:Computation of the transformation semigroups on three letters. J. Austral. Math. Soc.14 (1972), 335.Google Scholar
  88. 88.
    Wilde, C., and Sh. Raney:The transformation semigroups on three letters. Mimeographed manuscr., approx. 1972.Google Scholar
  89. 89.
    Wilde, C.:Characterization of finite amenable transformation semigroups. J. Austral. Math. Soc.15 (1973), 86–93.Google Scholar

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© Springer-Verlag New York Inc. 1977

Authors and Affiliations

  • H. Jürgensen
    • 1
  1. 1.Technische Hochschule DarmstadtInstitut für Theoretische InformatikDarmstadtGermany

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