“School of Mathematics”
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| Paper IPM / M / 7715 |
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| Abstract: | |
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A cover for a group G is a collection of proper subgroups whose
union is the whole group G. A cover is irredundant if no proper
sub-collection is also a cover and is called maximal if all its
members are maximal subgroups. For an integer n > 2, a cover with
n members is called an n−cover. Also we denote σ(G)=n if
G has an n-cover and does not have any m-cover for each
integer m < n. In this paper we completely characterize groups
with a maximal irredunadant 6-cover with core-free intersection.
As an application of this result, we characterize the groups G
with σ(G)=6. The intersection of an irredundant n−cover
is known to have index bounded by a function of n, though in
general the precise bound is not known. We prove also that, the
exact bound is 36 when n is 6.
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