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L. G. KOVÁCS AND LINEAR GROUPS

Part of: Structure and classification of infinite or finite groups Other groups of matrices

Published online by Cambridge University Press:  12 May 2016

A. S. DETINKO  and
D. L. FLANNERY
A. S. DETINKO
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland email alla.detinko@nuigalway.ie
D. L. FLANNERY*
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland email dane.flannery@nuigalway.ie
*
✉dane.flannery@nuigalway.ie
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Abstract

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

Keywords

linear groupclassificationalgorithm

MSC classification

Primary: 20H20: Other matrix groups over fields
Secondary: 20E45: Conjugacy classes 20E99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 1 , February 2017 , pp. 55 - 62
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Bácskai, Z., ‘Finite irreducible monomial groups of small prime degree’, PhD Thesis, Australian National University, 1999.Google Scholar
Blichfeldt, H. F., Finite Collineation Groups (University of Chicago Press, Chicago, 1917).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.CrossRefGoogle Scholar
Conlon, S. B., ‘ p-groups with an abelian maximal subgroup and cyclic center’, J. Aust. Math. Soc. Ser. A 22(2) (1976), 221–233.Google Scholar
Coutts, H. J., Quick, M. and Roney-Dougal, C., ‘The primitive permutation groups of degree less than 4096’, Comm. Algebra 39(10) (2011), 3526–3546.Google Scholar
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), 942–950.Google Scholar
Detinko, A. S., Eick, B. and Flannery, D. L., Nilmat—Computing with nilpotent matrix groups. http://www.gap-system.org/Packages/nilmat.html.Google Scholar
Detinko, A. S. and Flannery, D. L., ‘Classification of nilpotent primitive linear groups over finite fields’, Glasg. Math. J. 46(3) (2004), 585–594.Google Scholar
Dixon, J. D. and Kovács, L. G., ‘Generating finite nilpotent irreducible linear groups’, Q. J. Math. Oxford Ser. (2) 44(173) (1993), 1–15.CrossRefGoogle Scholar
Dixon, J. D. and Mortimer, B., ‘The primitive permutation groups of degree less than 1000’, Math. Proc. Cambridge Philos. Soc. 103(2) (1988), 213–238.Google Scholar
Dixon, J. D. and Zalesskii, A. E., ‘Finite primitive linear groups of prime degree’, J. Lond. Math. Soc. (2) 57(1) (1998), 126–134.Google Scholar
Dixon, J. D. and Zalesskii, A. E., ‘Finite imprimitive linear groups of prime degree’, J. Algebra 276(1) (2004), 340–370.Google Scholar
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), 808–812.Google Scholar
Eick, B. and Höfling, B., ‘The solvable primitive permutation groups of degree at most 6560’, LMS J. Comput. Math. 6 (2003), 29–39; (electronic).CrossRefGoogle Scholar
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), 55–93.Google Scholar
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), 397–407.Google Scholar
Flannery, D. L., The Finite Irreducible Linear 2-groups of Degree 4, Memoirs of the American Mathematical Society (American Mathematical Society, Providence, RI, 1997).Google Scholar
Flannery, D. L., ‘The finite irreducible monomial linear groups of degree 4’, J. Algebra 218(2) (1999), 436–469.Google Scholar
Flannery, D. L. and O’Brien, E. A., ‘Linear groups of small degree over finite fields’, Internat. J. Algebra Comput. 15(3) (2005), 467–502.Google Scholar
Höfling, B., ‘Finite irreducible imprimitive nonmonomial complex linear groups of degree 4’, J. Algebra 236(2) (2001), 419–470.Google Scholar
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), 207–218.Google Scholar
Kovács, L. G., ‘On tensor induction of group representations’, J. Aust. Math. Soc. Ser. A 49(3) (1990), 486–501.Google Scholar
Kovács, L. G., ‘Semigroup algebras of the full matrix semigroup over a finite field’, Proc. Amer. Math. Soc. 116(4) (1992), 911–919.Google Scholar
Kovács, L. G. and Robinson, G. R., ‘Generating finite completely reducible linear groups’, Proc. Amer. Math. Soc. 112(2) (1991), 357–364.CrossRefGoogle Scholar
Kovács, L. G. and Sim, H.-S., ‘Generating finite soluble groups’, Indag. Math. (N.S.) 2(2) (1991), 229–232.Google Scholar
Kovács, L. G. and Sim, H.-S., ‘Nilpotent metacyclic irreducible linear groups of odd order’, Arch. Math. (Basel) 65(4) (1995), 281–288.Google Scholar
Robinson, G. R., ‘The work of L.G. Kovács on representation theory’, J. Aus. Math. Soc., to appear. Published online (16 June 2015).Google Scholar
Short, M. W., The Primitive Soluble Permutation Groups of Degree Less than 256, Lecture Notes in Mathematics, 1519 (Springer, Berlin, 1992).Google Scholar
Sim, H.-S., ‘Metacyclic primitive linear groups’, Comm. Algebra 22(1) (1994), 269–278.Google Scholar
Suprunenko, D. A., Matrix Groups, Translations of Mathematical Monographs, Vol. 45 (American Mathematical Society, Providence, RI, 1976).CrossRefGoogle Scholar
Suprunenko, D. A., Permutation Groups (Navyka i Technika, Minsk, 1996), (in Russian).Google Scholar
Zalesskii, A. E., ‘Linear groups’, Russian Math. Surveys 36(5) (1981), 63–128.Google Scholar
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.).Google Scholar
Zalesskii, A. E., ‘Linear groups’, in: Algebra IV, Encyclopaedia Math. Sci., Vol. 37 (Springer, Berlin, 1993), 97–196.Google Scholar