A note on minimal coverings of groups by subgroups

Authors
Bryce, RA Serena, L
Citation
Ra. Bryce et L. Serena, A note on minimal coverings of groups by subgroups, J AUS MAT A, 71, 2001, pp. 159-168
Citations number
12
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
02636115 → ACNP
Volume
71
Year of publication
2001
Part
2
Pages
159 - 168
Database
ISI
SICI code
0263-6115(200110)71:<159:ANOMCO>2.0.ZU;2-F
Abstract
A cover for a group is a finite set of subgroups whose union is the whole g roup. A cover is minimal if its cardinality is minimal. Minimal covers of f inite 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.