Huppert's Conjecture for finite simple exceptional groups of Lie type

Hung P. Tong-Viet

Huppert's Conjecture for finite simple exceptional groups of Lie type

Group Theory 2024-10-29 v3 Representation Theory

Authors: Hung P. Tong-Viet

Abstract

Let $G$ be a finite group and let $\textrm{cd}(G)$ be the set of all complex irreducible character degrees of $G.$ In this paper, we show that if $\textrm{cd}(G)=\textrm{cd}(H),$ where $H$ is a finite simple exceptional group of Lie type, then $G\cong H\times A,$ where $A$ is an abelian group. This completes the verification of Huppert's Conjecture for all finite simple exceptional groups of Lie type.

Keywords

character degrees finite simple groups exceptional groups Huppert conjecture Lie type

Cite

@article{arxiv.2405.07422,
  title  = {Huppert's Conjecture for finite simple exceptional groups of Lie type},
  author = {Hung P. Tong-Viet},
  journal= {arXiv preprint arXiv:2405.07422},
  year   = {2024}
}

Comments

18 pages. Some typos are corrected

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