Non abelian tensor square of non abelian prime power groups

Details Non abelian tensor square of non abelian prime power groups Non abelian tensor square of non abelian prime power groups

2010-12-16

arxiv.org/abs/1012.3738v1

Mathematics

Group Theory

Scientific paper

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 $\pi_3(SK(G, 1))$.

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