Classification of p-groups by their Schur multiplier

Sumana Hatui

Published 2016-05-06Version 1

Let $G$ be a non-abelian $p$-group of order $p^n$ and $M(G)$ be its Schur multiplier. It is well known result by Green that $|M(G)| \leq p^{\frac{1}{2}n(n-1)}$. So $|M(G)|= p^{\frac{1}{2}n(n-1)-t(G)}$ for $t(G) \geq 0$. The groups has already been classified for $t(G) \leq 5$ by several authors. In this paper the classification of groups $G$ is determined for $t(G) = 6$.