Characterization of finite $p$-groups by their Schur multiplier

Proceedings of the Indian Academy of Sciences. Mathematical sciences

SUMANA HATUI^1,2¹ 

[1] School of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India^1;Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400 085, India^2

关键词: Schur multiplier;    finite p-groups;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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

【 授权许可】

CC BY