On groups with the same character degrees as almost simple groups with socle small Ree groups

2023/03/07 by Seyed Hassan Alavi, Alavi, Seyed Hassan
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2303.03607

openalex publication_date 2023/03/07 · openalex created_date 2023/03/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group and \rm cd(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group with socle H₀= ²\rm G₂(q), where q=3^f with f≥ 3 odd such that \rm cd(G)=\rm cd(H), then G is non-solvable and the chief factor G'/M of G is isomorphic to H₀. If, in particular, f is coprime to 3, then G' is isomorphic to H₀ and G/\bf Z(G) is isomorphic to H.

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