Projective special linear groups $PSL_4(q)$ are determined by the set of their character degrees

Hung Ngoc Nguyen; Hung P. Tong-Viet; Thomas P. Wakefield

Projective special linear groups $PSL_4(q)$ are determined by the set of their character degrees

Group Theory 2015-02-02 v3 Representation Theory

Authors: Hung Ngoc Nguyen , Hung P. Tong-Viet , Thomas P. Wakefield

Abstract

Let $G$ be a finite group and let $cd(G)$ be the set of all irreducible complex character degrees of $G$ . It was conjectured by Huppert in Illinois J. Math. 44 (2000) that, for every non-abelian finite simple group $H$ , if $cd(G)=cd(H)$ then $G\cong H\times A$ for some abelian group $A$ . In this paper, we confirm the conjecture for the family of projective special linear groups $\textrm{PSL}_4(q)$ with $q\geq 13$ .

Keywords

character degrees projective special linear group Huppert's conjecture finite simple group PSL_4(q)

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@article{arxiv.1108.0010,
  title  = {Projective special linear groups $PSL_4(q)$ are determined by the set of their character degrees},
  author = {Hung Ngoc Nguyen and Hung P. Tong-Viet and Thomas P. Wakefield},
  journal= {arXiv preprint arXiv:1108.0010},
  year   = {2015}
}

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26 pages

Projective special linear groups $PSL_4(q)$ are determined by the set of their character degrees

Abstract

Keywords

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