Non abelian tensor square of non abelian prime power groups

Abstract

For every $p$-group of order $p^n$ with the derived subgroup of order $p^m$, Rocco in \cite{roc} has shown that the order of tensor square of $G$ is at most $p^{n(n-m)}$. In the present paper not only we improve his bound for non-abelian $p$-groups but also we describe the structure of all non-abelian $p$-groups when the bound is attained for a special case. Moreover, our results give as well an upper bound for the order of ${\pi }_3(SK(G,1))$.

enriched with contributions of F.G. Russo

Cited by in corpus (3)

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