Abelian quotients and orbit sizes of finite groups

2014/07/24 by Thomas Michael Keller, Yong Yang, Keller, Thomas Michael +1
Computer Science · Mathematics · #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.1407.6436

openalex publication_date 2014/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group, and let V be a completely reducible faithful G-module. It has been known for a long time that if G is abelian, then G has a regular orbit on V. In this paper we show that G has an orbit of size at least |G/G'| on V. This generalizes earlier work of the authors, where the same bound was proved under the additional hypothesis that G is solvable. For completely reducible modules it also strengthens the 1989 result |G/G'|

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