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Paper   IPM / M / 7715
School of Mathematics
  Title:   Groups with a maximal irredundant 6-cover
  Author(s):  A. Abdollahi (joint with M. J. Ataei, S.M . Jafarian Amiri and A. Mohammadi Hassanabadi )
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  33
  Year:  2005
  Pages:   3225-3238
  Supported by:  IPM
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 ncover. 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 ncover 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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