A group is covered by a collection of subgroups if it is the union of the collection. The intersection of an irredundant cover of n subgroups is known to have index bounded by a function of n, though in general the precise bound is not known. Here we confirm a claim of Tompkinson that the correct bound is 16 when n is 5. The proof depends on determining all the 'minimal' groups with an irredundant cover of five maximal subgroups.
Covering groups with subgroups / R. A. Bryce; V. Fedri; L. Serena. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - STAMPA. - 55:(1997), pp. 469-476. [10.1017/s0004972700034109]
Covering groups with subgroups
SERENA, LUIGI
1997
Abstract
A group is covered by a collection of subgroups if it is the union of the collection. The intersection of an irredundant cover of n subgroups is known to have index bounded by a function of n, though in general the precise bound is not known. Here we confirm a claim of Tompkinson that the correct bound is 16 when n is 5. The proof depends on determining all the 'minimal' groups with an irredundant cover of five maximal subgroups.
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