Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T09:24:41.977Z Has data issue: false hasContentIssue false
  • English
  • Français

Fixed Point Free Actions of Groups of Exponent 5

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Enrico Jabara
Enrico Jabara
Affiliation:
Dipartimento di Informatica, Universitá di Ca' Foscari, Via Torino 155–30174 Venezia, Italy e-mail: [email protected]
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.

In this paper we prove that if V is a vector space over a field of positive characteristric p ≠ 5 then any regular subgroup A of exponent 5 of GL(V) is cyclic. As a consequence a conjecture of Gupta and Mazurov is proved to be true.

MSC classification

Secondary: 20E25: Local properties 20F50: Periodic groups; locally finite groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 3 , December 2004 , pp. 297 - 304
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Adyan, S. I., ‘Periodic groups of odd exponent’, in: Proceedings of the Second International Conference on the Theory of Groups, Australian Nat. Univ., 1973, Lecture Notes in Math. 372 (Springer, Berlin, 1974) pp. 8–12.Google Scholar
[2]Gupta, N. D. and Mazurov, V. D., ‘On groups with small orders of elements’, Bull. Austral. Math. Soc. 60 (1999), 197–205.Google Scholar
[3]Hall, M., ‘Solution of the Burnside problem for exponent six’, Illinois J. Math. 2 (1958), 764–786.Google Scholar
[4]Levi, F. W. and van der Waerden, B. L., ‘Über eine besondere Klasse von Gruppen’, Abh. Math. Sem. Univ. Hamburg 9 (1932), 154–158.Google Scholar
[5]Mazurov, V. D., ‘Groups of exponent 60 with prescribed orders of elements’, Algebra i Logika 39 (2000), 329–346; English translation: Algebra and Logic 39 (2000), 189–198.Google Scholar
[6]Neumann, B. H., ‘Groups whose elements have bounded orders’, J. London Math. Soc. 12 (1937), 195–198.CrossRefGoogle Scholar
[7]Ol'šanskii, A. Ju., ‘An infinite group with subgroups of prime order’, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 309–321.Google Scholar
[8]Robinson, D. J. S., A course in the theory of groups (Springer, Berlin, 1982).CrossRefGoogle Scholar
[9]Sanov, I. N., ‘Solution of Burnside's problem for exponent 4’, Leningrad Univ. Ann. Math. Ser. 10 (1940), 166–170.Google Scholar
[10]Zhurtov, A. K. and Mazurov, V. D., ‘A recognition of simple groups L2(2m) in the class of all groups’, Sibirsk. Math. Zh. 40 (1999), 75–78;Google Scholar
English translation: Siberian Math. J. 40 (1999), 62–64.Google Scholar