Characterization of Finite p-Groups by Their Non-Abelian Tensor Square

Abstract

Let G be a finite p-group of order p n with |G′| =p c and G ⊗ G be the non-abelian tensor square of G. In 1991, Rocco proved that |G ⊗ G| =p n(n−c)−l for some integer l ≥ 0. In this article we characterize all finite p-groups, for which |G′| =p and 0 ≤ l ≤ 10.