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A note on minimal coverings of groups by subgroups

Part of: Representation theory of groups Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  09 April 2009

R. A. Bryce  and
L. Serena
R. A. Bryce
Affiliation:
School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia e-mail: [email protected]
L. Serena
Affiliation:
Dipartimento di Matematica, e Applicazioni per l'Architettura, Università di Firenze, Piazza Ghiberti 27, 50122 Firenze, Italia e-mail: [email protected]
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Abstract

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A cover for a group is a finite set of subgroups whose union is the whole group. A cover is minimal if its cardinality is minimal. Minimal covers of finite soluble groups are categorised; in particular all but at most one of their members are maximal subgroups. A characterisation is given of groups with minimal covers consisting of abelian subgroups.

MSC classification

Secondary: 17B01: Identities, free Lie (super)algebras 20C20: Modular representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 2 , October 2001 , pp. 159 - 168
Copyright
Copyright © Australian Mathematical Society 2001

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