Covering Groups With Subgroups

Mathematics Research Report MRR95-082

Covering Groups With Subgroups

R.A. Bryce, V. Fedri and L. Serena

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 M. J. Tompkinson (Groups covered by finitely many cosets or subgroups, Comm. Alg. 15 (1987), 845-859) that for n=5 the correct bounded is 16. We also determine all groups with an iredundant cover of five maximal subgroups whose intersection is core-free.

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