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

The concept of isoclinism on the class of all pairs of groups (G,N) GN in which N is a normal subgroup of G, isintroduced and also some properties of this notion are studied by some authors. In this paper, using thisnotion, the set of all pairs (G,φ(G)) of p-groups of order at most p۴ is classified. Meanwhile, a fullclassification of pairs (G,φ(G)) of extra special p-groups is also given.

Keywords:

Isoclinism , Frattini subgroup , Pairs of groups