University of KashanMathematics Interdisciplinary Research2538-36393220181201A Simple Classification of Finite Groups of Order p2q289984527310.22052/mir.2017.62726.1044ENAzizSeyyed HadiDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training UniversityModjtabaGhorbaniDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training UniversityFarzanehNowroozi LarkiDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training UniversityJournal Article20160424Suppose G is a group of order p<sup>2</sup>q<sup>2</sup> 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 p<sup>2</sup>q<sup>2</sup> when Q and P are cyclic, three groups when Q is a cyclic and P is an elementary ablian group, p<sup>2</sup>+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.https://mir.kashanu.ac.ir/article_45273_e39c942af529952ba55f29606887d4c6.pdf