Characterizing finite $p$-groups by their Schur multipliers

Abstract

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 $t(G)\ge 0$. 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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• On twisted group ring isomorphism problem for p-groups
• On the Order of the Schur Multiplier of a Pair of Finite p-Groups
• Classification of $p$-groups via their $2$-nilpotent multipliers