Hostname: page-component-89b8bd64d-72crv Total loading time: 0 Render date: 2026-05-08T21:10:06.640Z Has data issue: false hasContentIssue false
  • English
  • Français

THE CONTRIBUTION OF L. G. KOVÁCS TO THE THEORY OF PERMUTATION GROUPS

Part of: Structure and classification of infinite or finite groups Permutation groups

Published online by Cambridge University Press:  05 November 2015

CHERYL E. PRAEGER  and
CSABA SCHNEIDER
CHERYL E. PRAEGER
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, 6009 Crawley, Western Australia email cheryl.praeger@uwa.edu.au
CSABA SCHNEIDER*
Affiliation:
Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG, Brazil email csaba@mat.ufmg.br
*
✉ csaba@mat.ufmg.br
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

The work of L. G. (Laci) Kovács (1936–2013) gave us a deeper understanding of permutation groups, especially in the O’Nan–Scott theory of primitive groups. We review his contribution to this field.

Keywords

L. G. Kovácspermutation groupsmaximal subgroupsO’Nan–Scott theorem

MSC classification

Primary: 20E28: Maximal subgroups
Secondary: 20B15: Primitive groups 20B99: None of the above, but in this section

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 1 , February 2017 , pp. 20 - 33
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Aschbacher, M. and Guralnick, R. M., ‘On abelian quotients of primitive groups’, Proc. Amer. Math. Soc. 107(1) (1989), 89–95.Google Scholar
Aschbacher, M. and Scott, L., ‘Maximal subgroups of finite groups’, J. Algebra 92(1) (1985), 44–80.Google Scholar
Baddeley, R. W., ‘Primitive permutation groups with a regular nonabelian normal subgroup’, Proc. Lond. Math. Soc. (3) 67(3) (1993), 547–595.Google Scholar
Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system I: the user language’, J. Symbolic Comput. 24 (1997), 235–265.Google Scholar
Breuer, T., ‘Subgroups of J 4 inducing the same permutation character’, Comm. Algebra 23(9) (1995), 3173–3176.Google Scholar
Bryant, R. M., Kovács, L. G. and Robinson, G. R., ‘Transitive permutation groups and irreducible linear groups’, Q. J. Math. Oxford Ser. (2) 46(184) (1995), 385–407.Google Scholar
Cameron, P. J., Permutation Groups, London Mathematical Society Student Texts, 45 (Cambridge University Press, Cambridge, 1999).Google Scholar
Cameron, P. J., Kovács, L. G., Newman, M. F. and Praeger, C. E., ‘Fixed-point-free permutations in transitive permutation groups of prime-power order’, Q. J. Math. Oxford Ser. (2) 36(143) (1985), 273–278.Google Scholar
Cannon, J. and Holt, D. F., ‘Computing maximal subgroups of finite groups’, J. Symbolic Comput. 37(5) (2004), 589–609.Google Scholar
Cooperstein, B. and Mason, G. (eds.), The Santa Cruz Conference on Finite Groups, University of California, Santa Cruz, CA, 25 June–20 July 1979, Proceedings of Symposia in Pure Mathematics, 37 (American Mathematical Society, Providence, RI, 1980).Google Scholar
Eick, B. and Hulpke, A., ‘Computing the maximal subgroups of a permutation group. I.’, Groups and Computation III, Proc. Int. Conf., Ohio State University, Columbus, OH, 15–19 June 1999 (Walter de Gruyter, Berlin, 2001), 155–168.Google Scholar
Förster, P. and Kovács, L. G., ‘Finite primitive groups with a single non-abelian regular normal subgroup’, Research Report 17, Australian National University, School of Mathematical Sciences, 1989.Google Scholar
Förster, P. and Kovács, L. G., ‘A problem of Wielandt on finite permutation groups’, J. Lond. Math. Soc. (2) 41(2) (1990), 231–243.Google Scholar
Franchi, C., ‘On minimal degrees of permutation representations of abelian quotients of finite groups’, Bull. Aust. Math. Soc. 84(3) (2011), 408–413.Google Scholar
Gross, F. and Kovács, L. G., ‘On normal subgroups which are direct products’, J. Algebra 90(1) (1984), 133–168.Google Scholar
Guralnick, R. M. and Saxl, J., ‘Primitive permutation characters’, Groups, Combinatorics and Geometry, Proc. LMS Durham Symp., Durham, UK, 5–15 July 1990 (Cambridge University Press, Cambridge, 1992), 364–367.Google Scholar
Holt, D. F. and Walton, J., ‘Representing the quotient groups of a finite permutation group’, J. Algebra 248(1) (2002), 307–333.Google Scholar
Jordan, C., Traité des Substitutions et des Équationes Algébriques (Gauthier-Villars, Paris, 1870).Google Scholar
Kovács, L. G., ‘Maximal subgroups in composite finite groups’, J. Algebra 99(1) (1986), 114–131.Google Scholar
Kovács, L. G., ‘Primitive permutation groups of simple diagonal type’, Israel J. Math. 63(1) (1988), 119–127.CrossRefGoogle Scholar
Kovács, L. G., ‘Wreath decompositions of finite permutation groups’, Bull. Aust. Math. Soc. 40 (1989), 255–279.Google Scholar
Kovács, L. G., ‘Primitive subgroups of wreath products in product action’, Proc. Lond. Math. Soc. (3) 58(2) (1989), 306–322.Google Scholar
Kovács, L. G. and Newman, M. F., ‘Generating transitive permutation groups’, Q. J. Math. Oxford Ser. (2) 39(155) (1988), 361–372.Google Scholar
Kovács, L. G. and Praeger, C. E., ‘Finite permutation groups with large abelian quotients’, Pacific J. Math. 136(2) (1989), 283–292.Google Scholar
Kovács, L. G. and Praeger, C. E., ‘On minimal faithful permutation representations of finite groups’, Bull. Aust. Math. Soc. 62(2) (2000), 311–317.Google Scholar
Kovács, L. G. and Robinson, G. R., ‘On the number of conjugacy classes of a finite group’, J. Algebra 160(2) (1993), 441–460.Google Scholar
Liebeck, M. W., Praeger, C. E. and Saxl, J., ‘On the O’Nan–Scott theorem for finite primitive permutation groups’, J. Aust. Math. Soc. A 44(3) (1988), 389–396.CrossRefGoogle Scholar
Lucchini, A., Menegazzo, F. and Morigi, M., ‘Asymptotic results for transitive permutation groups’, Bull. Lond. Math. Soc. 32(2) (2000), 191–195.CrossRefGoogle Scholar
Maróti, A. and Garonzi, M., ‘On the number of conjugacy classes of a permutation group’, J. Combin Theory Ser. A 133 (2015), 251–260.Google Scholar
Neumann, P. M., ‘Some algorithms for computing with finite permutation groups’, in: Proceedings of Groups—St. Andrews 1985, London Mathematical Society Lecture Note Series, 121 (Cambridge University Press, Cambridge, 1986), 59–92.Google Scholar
Praeger, C. E., ‘The inclusion problem for finite primitive permutation groups’, Proc. Lond. Math. Soc. (3) 60(1) (1990), 68–88.Google Scholar
Scott, L. L., ‘Representations in characteristic $p$ ’, in [ CM80 , pages 319–331].Google Scholar