Characterizing finite $p$-groups by their Schur multipliers

Details Characterizing finite $p$-groups by their Schur multipliers Characterizing finite $p$-groups by their Schur multipliers

2010-01-24

arxiv.org/abs/1001.4256v1

Mathematics

Group Theory

Scientific paper

It has been proved in \cite{ge} for every $p$-group of order $p^n$, $|\mathcal{M}(G)|=p^{\f{1}{2}n(n-1)-t(G)}$, where $t(G)\geq 0$. In \cite{be, el, zh}, the structure of $G$ has been characterized for $t(G)=0,1,2,3$ by several authors. Also in \cite{sa}, the structure of $G$ characterized when $t(G)=4$ and $Z(G)$ is elementary abelian. This paper is devoted to classify the structure of $G$ when $t(G)=4$ without any condition.

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