On the characterization of some non-abelian simple groups using codegree set

2022/11/10 by Wang, Hongning, Zhang, Xuning, Zhang, Selina +1
#20C15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2211.05287

Abstract

Let G be a finite group and χ∈ \irr(G). The codegree of χ is defined as \cod(χ)=(|G:ker(χ)|)/(χ(1)) and \cod(G)=\\cod(χ) | χ∈ \irr(G)\ is called the set of codegrees of G. In this paper, we show that the set of codegrees of \Sy₄(4), \U₄(2), \Sy₄(q) (q ≥ 4), \U₄(3), ²\F₄(2)', \J₃, \G₂(3), \A₉, \J₂, \PSL(4,3), \McL, \Sy₄(5), \G₂(4), \HS, \ON and \M₂₄ determines the group up to isomorphism.

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• A characterization of some finite simple groups by their character codegrees
• The codegree isomorphism problem for finite simple groups II
• On the Characterization of Sporadic Simple Groups by Codegrees
• On the Characterization of Alternating Groups by Codegrees