ON THE CLASSIFICATION OF SOME PAIRS ( , ( )) G G  OF P-GROUPS

Abstract

The concept of isoclinism on the class of all pairs of groups ( , ) G N in which N is a normal subgroup of G, is introduced and also some properties of this notion are studied by some authors. In this paper, using this notion, the set of all pairs ( , ( )) G G  of p-groups of order at most 4 p is classified. Meanwhile, a full classification of pairs ( , ( )) G G  of extra special p-groups is also given.