A characterization of finite $p$-groups by their Schur multiplier

Sumana Hatui

A characterization of finite $p$-groups by their Schur multiplier

Group Theory 2017-03-21 v2

Authors: Sumana Hatui

Abstract

Let $G$ be a finite $p$ -group of order $p^n$ and $M(G)$ be its Schur multiplier. It is well known result by Green that $|M(G)|= p^{\frac{1}{2}n(n-1)-t(G)}$ for some $t(G) \geq 0$ . In this article we classify non-abelian $p$ -groups $G$ of order $p^n$ for $t(G)=\log_p(|G|)+1$ .

Keywords

finite p-groups Schur multiplier group classification non-abelian groups group order Green's theorem

Cite

@article{arxiv.1608.06322,
  title  = {A characterization of finite $p$-groups by their Schur multiplier},
  author = {Sumana Hatui},
  journal= {arXiv preprint arXiv:1608.06322},
  year   = {2017}
}

Comments

Accepted in Proc. Indian Acad. Sci. Math. Sci

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