A Simple Classification of Finite Groups of Order p2q2

Abstract

‎Suppose G is a group of order p2q2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, ‎respectively‎. ‎In this paper‎, ‎we show that up to isomorphism‎, ‎there are four groups of order p2q2 when Q and P are cyclic‎, ‎three groups when Q is a cyclic and P is an elementary ablian group‎, ‎p2+3p/2+7 groups when Q is an elementary ablian group and P is a cyclic group and finally‎, ‎p‎ + ‎5 groups when both Q and P are elementary abelian groups.‎

Keywords

• semi-direct product‎
• ‎p-group‎
• ‎sylow subgroup