On the non-abelian tensor square of groups of order dividing $p^{5}$

Abstract

In this paper we consider all groups of order dividing $p^5$. We obtain the explicit structure of the non-abelian tensor square, non-abelian exterior square, tensor center, exterior center, the third homotopy group of suspension of an Eilenberg-MacLain space $k(G,1) $ and $\triangledown(G)$ of such groups.