Abstract
Let S be a subgroup of a group G. A set Π={H1,…,Hn} of subgroups Hi(i=1,…,n) with G=∪Hi∈ΠHi is said to be an equal quasi-partition of G if Hi∩Hj≅S and |Hi|=|Hj| for all Hi,Hj∈Π with i≠j. In this paper we investigate finite p-groups such that a subset of their maximal subgroups form an equal quasi-partition.