A generalization of Szep's conjecture for almost simple groups

2022/08/18 by Nick Gill, Michael Giudici, Gill, Nick +3 · 1 citation
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2208.08763

openalex publication_date 2022/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a natural generalization of Szep's conjecture. Given an almost simple group G with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements x,y∈ G∖\1\ with G=\bf N_G (⟨ x⟩)\bf N_G(⟨ y⟩), where we are denoting by \bf N_G(⟨ x⟩) and by \bf N_G(⟨ y⟩) the normalizers of the cyclic subgroups ⟨ x⟩ and ⟨ y⟩. As a consequence of this result, we classify all possible group elements x,y∈ G∖\1\ with G=\bf C_G(x)\bf C_G(y).

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• Groups with conjugacy classes of coprime sizes

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