Skip to main content


  • A. S. DETINKO (a1) and D. L. FLANNERY (a2)

We survey the legacy of L. G. Kovács in linear group theory, with a particular focus on classification questions.

Corresponding author
Hide All
[1] Bácskai, Z., ‘Finite irreducible monomial groups of small prime degree’, PhD Thesis, Australian National University, 1999.
[2] Blichfeldt, H. F., Finite Collineation Groups (University of Chicago Press, Chicago, 1917).
[3] 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), 385407.
[4] Conlon, S. B., ‘ p-groups with an abelian maximal subgroup and cyclic center’, J. Aust. Math. Soc. Ser. A 22(2) (1976), 221233.
[5] Coutts, H. J., Quick, M. and Roney-Dougal, C., ‘The primitive permutation groups of degree less than 4096’, Comm. Algebra 39(10) (2011), 35263546.
[6] Detinko, A. S., ‘A new GAP group library for irreducible maximal solvable subgroups of prime degree classical groups’, J. Math. Sci. (N.Y.) 108(6) (2002), 942950.
[7] Detinko, A. S., Eick, B. and Flannery, D. L., Nilmat—Computing with nilpotent matrix groups.
[8] Detinko, A. S. and Flannery, D. L., ‘Classification of nilpotent primitive linear groups over finite fields’, Glasg. Math. J. 46(3) (2004), 585594.
[9] Dixon, J. D. and Kovács, L. G., ‘Generating finite nilpotent irreducible linear groups’, Q. J. Math. Oxford Ser. (2) 44(173) (1993), 115.
[10] Dixon, J. D. and Mortimer, B., ‘The primitive permutation groups of degree less than 1000’, Math. Proc. Cambridge Philos. Soc. 103(2) (1988), 213238.
[11] Dixon, J. D. and Zalesskii, A. E., ‘Finite primitive linear groups of prime degree’, J. Lond. Math. Soc. (2) 57(1) (1998), 126134.
[12] Dixon, J. D. and Zalesskii, A. E., ‘Finite imprimitive linear groups of prime degree’, J. Algebra 276(1) (2004), 340370.
[13] Dixon, J. D. and Zalesskii, A. E., ‘Corrigendum: “Finite primitive linear groups of prime degree” [J. Lond. Math. Soc. (2) 57 (1998), no. 1, 126–134]’, J. Lond. Math. Soc. (2) 77(3) (2008), 808812.
[14] Eick, B. and Höfling, B., ‘The solvable primitive permutation groups of degree at most 6560’, LMS J. Comput. Math. 6 (2003), 2939; (electronic).
[15] Feit, W., ‘The current situation in the theory of finite simple groups’, in: Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1 (Gauthier-Villars, Paris, 1971), 5593.
[16] Feit, W., ‘On finite linear groups in dimension at most 10’, in: Proceedings of the Conference on Finite Groups (Univ. Utah, Park City, Utah, 1975) (Academic Press, New York, 1976), 397407.
[17] Flannery, D. L., The Finite Irreducible Linear 2-groups of Degree 4, Memoirs of the American Mathematical Society (American Mathematical Society, Providence, RI, 1997).
[18] Flannery, D. L., ‘The finite irreducible monomial linear groups of degree 4’, J. Algebra 218(2) (1999), 436469.
[19] Flannery, D. L. and O’Brien, E. A., ‘Linear groups of small degree over finite fields’, Internat. J. Algebra Comput. 15(3) (2005), 467502.
[20] Höfling, B., ‘Finite irreducible imprimitive nonmonomial complex linear groups of degree 4’, J. Algebra 236(2) (2001), 419470.
[21] Kovács, L. G., ‘Some representations of special linear groups’, in: The Arcata Conference on Representations of Finite Groups (Arcata, CA, 1986), Proceedings of Symposia in Pure Mathematics, 47, Part 2 (American Mathematical Society, Providence, RI, 1987), 207218.
[22] Kovács, L. G., ‘On tensor induction of group representations’, J. Aust. Math. Soc. Ser. A 49(3) (1990), 486501.
[23] Kovács, L. G., ‘Semigroup algebras of the full matrix semigroup over a finite field’, Proc. Amer. Math. Soc. 116(4) (1992), 911919.
[24] Kovács, L. G. and Robinson, G. R., ‘Generating finite completely reducible linear groups’, Proc. Amer. Math. Soc. 112(2) (1991), 357364.
[25] Kovács, L. G. and Sim, H.-S., ‘Generating finite soluble groups’, Indag. Math. (N.S.) 2(2) (1991), 229232.
[26] Kovács, L. G. and Sim, H.-S., ‘Nilpotent metacyclic irreducible linear groups of odd order’, Arch. Math. (Basel) 65(4) (1995), 281288.
[27] Robinson, G. R., ‘The work of L.G. Kovács on representation theory’, J. Aus. Math. Soc., to appear. Published online (16 June 2015).
[28] Short, M. W., The Primitive Soluble Permutation Groups of Degree Less than 256, Lecture Notes in Mathematics, 1519 (Springer, Berlin, 1992).
[29] Sim, H.-S., ‘Metacyclic primitive linear groups’, Comm. Algebra 22(1) (1994), 269278.
[30] Suprunenko, D. A., Matrix Groups, Translations of Mathematical Monographs, Vol. 45 (American Mathematical Society, Providence, RI, 1976).
[31] Suprunenko, D. A., Permutation Groups (Navyka i Technika, Minsk, 1996), (in Russian).
[32] Zalesskii, A. E., ‘Linear groups’, Russian Math. Surveys 36(5) (1981), 63128.
[33] Zalesskii, A. E., ‘Linear groups’, Itogi Nauki i Tekhniki, Seriya Algebra,Topologiya, Geometriya, vol. 21 (1983), 135–182; J. Soviet Math. 31(3) (1985), 2974–3004 (English transl.).
[34] Zalesskii, A. E., ‘Linear groups’, in: Algebra IV, Encyclopaedia Math. Sci., Vol. 37 (Springer, Berlin, 1993), 97196.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed