Classification of p-groups by their Schur multiplier

2016/05/06 by Sumana Hatui, Hatui, Sumana
Computer Science · Mathematics · #20D15 #20E34 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1605.01849

openalex publication_date 2016/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a non-abelian p-group of order pⁿ and M(G) be its Schur multiplier. It is well known result by Green that |M(G)| ≤ p^{(1)/(2)n(n-1)}. So |M(G)|= p^{(1)/(2)n(n-1)-t(G)} for some t(G) ≥ 0. The groups has already been classified for t(G) ≤ 5 by several authors. For t(G)=6 the classification has been done. In this paper we classify p-groups G for t(G) = 6 in different method.

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