Classification of finite $p$-groups by the size of their Schur multipliers

Peyman Niroomand; Farangi Johari

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arXiv · 1706.02340

Classification of finite $p$-groups by the size of their Schur multipliers

Peyman Niroomand·Farangi Johari

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Abstract

Let $d(G)$ be the minimum number of elements required to generated a group $G.$ For a group $G $ of order $p^n$ with derived subgroup of order $ p^k $ and $d(G) = d,$ we knew the order of the Schur multiplier of $G$ is bounded by $ p^{\frac{1}{2}(d-1)(n-k+2)+1}. $ In the current paper, we find the structure of all $p$-groups that attains the mentioned bound. Moreover, we show that all of them are capable.

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BibTeX RIS

Peyman Niroomand, Farangi Johari. 2017-06-07. Classification of finite $p$-groups by the size of their Schur multipliers. https://arxiv.org/abs/1706.02340

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