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L. G. KOVÁCS AND VARIETIES OF GROUPS

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  13 May 2015

J. R. J. GROVES
J. R. J. GROVES*
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Australia email [email protected]
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Abstract

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This is a short account of some of the work of L. G. (Laci) Kovács on varieties of groups.

Keywords

Kovácsvarieties

MSC classification

Primary: 20E10: Quasivarieties and varieties of groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 1 , February 2017 , pp. 43 - 54
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Brisley, W. and Kovács, L. G., ‘On soluble groups of prime-power exponent’, Bull. Aust. Math. Soc. 4 (1971), 389–396.CrossRefGoogle Scholar
Bryant, R. M. and Kovács, L. G., ‘The skeleton of a variety of groups’, Bull. Aust. Math. Soc. 6 (1972), 357–378.CrossRefGoogle Scholar
Bryce, R. A., ‘Metabelian groups and varieties’, Philos. Trans. R. Soc. Lond. Ser. A 266 (1970), 281–355.Google Scholar
Fitzpatrick, P. and Kovács, L. G., ‘Varieties of nilpotent groups of class four. I’, J. Aust. Math. Soc. Ser. A 35(1) (1983), 59–73.CrossRefGoogle Scholar
Gupta, N. D. and Newman, M. F., ‘On metabelian groups’, J. Aust. Math. Soc. 6 (1966), 362–368.CrossRefGoogle Scholar
Hall, P. and Higman, G., ‘On the p-length of p-soluble groups and reduction theorems for Burnside’s problem’, Proc. Lond. Math. Soc. (3) 6 (1956), 1–42.CrossRefGoogle Scholar
Higman, G., ‘Representations of general linear groups and varieties of groups’, Proc. Int. Conf. on Theory of Groups Canberra, 1965 (Gordon and Breach, New York, 1967), 167–173.Google Scholar
Klyachko, A. A., ‘Varieties of p-groups of a small class’, Ordered Sets and Lattices 1 (1971), 31–42.Google Scholar
Klyachko, A. A., ‘Lie elements in a tensor algebra’, Sib. Math. J. 15 (1974), 914–921.Google Scholar
Kostrikin, A. I., ‘The Burnside problem’, Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 3–34.Google Scholar
Kovács, L. G., ‘Varieties and the Hall-Higman paper’, Proc. Int. Conf. on Theory of Groups Canberra, 1965 (Gordon and Breach, New York, 1967), 217–219.Google Scholar
Kovács, L. G., ‘On the number of varieties of groups’, J. Aust. Math. Soc. 8 (1968), 444–446.Google Scholar
Kovács, L. G., ‘Varieties and finite groups’, J. Aust. Math. Soc. 10 (1969), 5–19.Google Scholar
Kovács, L. G., ‘Varieties of nilpotent groups of small class’, in: Topics in Algebra (Proc. 18th Summer Res. Inst., Austral. Math. Soc., Austral. Nat. Univ., Canberra, 1978, Lecture Notes in Mathematics, 697 (Springer, Berlin, 1978), 205–229.Google Scholar
Kovács, L. G., ‘The thirty-nine varieties’, Math. Sci. 4(2) (1979), 113–128.Google Scholar
Kovács, L. G., ‘Classification theorems for torsion-free groups’, in: The Santa Cruz Conference on Finite Groups Univ. California, Santa Cruz, CA, 1979, Proceedings of Symposia in Pure Mathematics, 37 (American Mathematical Society, Providence, RI, 1980), 225–228.Google Scholar
Kovács, L. G. and Newman, M. F., ‘Cross varieties of groups’, Proc. Roy. Soc. Ser. A 292 (1966), 530–536.Google Scholar
Kovács, L. G. and Newman, M. F., ‘Minimal verbal subgroups’, Proc. Cambridge Philos. Soc. 62 (1966), 347–350.Google Scholar
Kovács, L. G. and Newman, M. F., ‘On critical groups’, J. Aust. Math. Soc. 6 (1966), 237–250.CrossRefGoogle Scholar
Kovács, L. G. and Newman, M. F., ‘Just-non-cross varieties’, Proc. Int. Conf. on Theory of Groups Canberra, 1965 (Gordon and Breach, New York, 1967) 221–223.Google Scholar
Kovács, L. G. and Newman, M. F., ‘On non-cross varieties of groups’, J. Aust. Math. Soc. 12 (1971), 129–144.Google Scholar
Kovács, L. G. and Newman, M. F., ‘Torsionfree varieties of metabelian groups’, in: Infinite Groups 1994 (Ravello) (de Gruyter, Berlin, 1996), 125–128.Google Scholar
Kovács, L. G., Newman, M. F. and Pentony, P. F., ‘Generating groups of nilpotent varieties’, Bull. Amer. Math. Soc. 74 (1968), 968–971.CrossRefGoogle Scholar
Kovács, L. G. and Stöhr, R., ‘A combinatorial proof of Klyachko’s theorem on Lie representations’, J. Algebraic Combin. 23(3) (2006), 225–230.Google Scholar
Neumann, B. H., ‘Identical relations in groups. I’, Math. Ann. 114(1) (1937), 506–525.Google Scholar
Neumann, H., Varieties of Groups (Springer, Berlin, 1967).CrossRefGoogle Scholar
Novikov, P. S. and Adjan, S. I., ‘Infinite periodic groups. I’, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 212–244.Google Scholar
Oates, S. and Powell, M. B., ‘Identical relations in finite groups’, J. Algebra 1 (1964), 11–39.Google Scholar
Ol’šanskiĭ, A. Ju., ‘The finite basis problem for identities in groups’, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 376–384.Google Scholar