Cosets of normal subgroups and union of two conjugacy classes

2025/08/08 by Antonio Beltrán, Beltrán, Antonio
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2508.06367

openalex publication_date 2025/08/08 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group, N a normal subgroup of G and x∈ G-N. We discuss when the coset Nx is contained in the union of two conjugacy classes, K and D, of G. We show that N need not be solvable, and can even be non-abelian simple, but in these cases, K and D must have the same cardinality, and the non-solvable structure of N is restricted. The non-abelian principal factors of G contained in N are then isomorphic to S× ⋯× S, where S is a simple group of Lie type of odd characteristic.

Citations

• Powers of conjugacy classes in a finite group

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• Fixed conjugacy classes of normal subgroups and the k(GV)-problem
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