A CONSTRUCTION OF P-GROUPS VIA WREATH PRODUCTS

Abstract

This research is essentially an upgrade or extension of the results of Audu on wreath product of permutation groups. In this work, a generalization of the concept of wreath product is considered based on the notion of an algebraic structure called Permutation group. Some basic procedures for computing wreath products of groups, the construction of groups as wreath products of cyclic groups and a generation of Sylow p-subgroups from resulting Cyclic groups areinvestigated. I mainly applied the concept of p-groups and wreath products of some groups of permutations to construct some groups of prime power order by taking p to be an arbitrary but fixed prime number, f... a finite set with n elements and G a permutation group on f....