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SOME REMARKS ON GROUPS WITH NILPOTENT MINIMAL COVERS

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 December 2008

R. A. BRYCE  and
L. SERENA
R. A. BRYCE*
Affiliation:
Department of Mathematics, The Australian National University, Canberra, ACT 0200, Australia (email: bryce@maths.anu.edu.au)
L. SERENA
Affiliation:
Dipartimento di Matematica e Applicazioni per l’Architettura, Universitá degli Studi di Firenze, piazza Ghiberti 27, 50122 Firenze, Italy (email: luigi.serena@unifi.it)
*
✉For correspondence; e-mail: bryce@maths.anu.edu.au
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Abstract

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A cover of a group is a finite collection of proper subgroups whose union is the whole group. A cover is minimal if no cover of the group has fewer members. It is conjectured that a group with a minimal cover of nilpotent subgroups is soluble. It is shown that a minimal counterexample to this conjecture is almost simple and that none of a range of almost simple groups are counterexamples to the conjecture.

Keywords

finite groupcover of a groupalmost simple group

MSC classification

Secondary: 20D99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 3 , December 2008 , pp. 353 - 365
Copyright
Copyright © Australian Mathematical Society 2009

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