UPPER BOUND OF SUM ELEMENTS ORDER FOR ۶-COVER GROUPS

A cover for a group G is a collection of proper subgroups whose union is the whole group G. A cover is irodundant if no proper sub-collection is also a cover, and is called maximal if all of the mnoubers are maximal subgroups, For an integer n>۲, a cover with n members is called an n-cover. In this paper we investigate the maximum value of Ψ on the set of groups with a maximal irredundant ۶-cover with core-free intersection.