A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is minimal if no other cover contains fewer members. We term minimised a minimal cover with the property that substituting for a member of the cover by a proper subgroup of that member produces a collection which is no longer a cover. We here describe the minimised covers for the groups GL2 (q), SL2 (q), PSL2 (q) and PGL2 (q).
Subgroup coverings of some linear groups / R.A. Bryce; V. Fedri; L. Serena. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - STAMPA. - 60:(1999), pp. 227-238. [10.1017/s0004972700036364]
Subgroup coverings of some linear groups
SERENA, LUIGI
1999
Abstract
A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is minimal if no other cover contains fewer members. We term minimised a minimal cover with the property that substituting for a member of the cover by a proper subgroup of that member produces a collection which is no longer a cover. We here describe the minimised covers for the groups GL2 (q), SL2 (q), PSL2 (q) and PGL2 (q).
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