Abstract
The aim of this article is to study the influence of a finite group of prime power order on the structure of specific types of algebras. In more details, we consider a finite group X = MG of prime power order and construct a bicrossproduct Hopf algebra associated with a factorization of this finite group X. Furthermore, we discuss which property of X can be carried out to the induced bicrossproduct Hopf algebra H = K(M) (sic) KG.