Projective special linear groups PSL₄(q) are determined by the set of their character degrees

2011/07/29 by Hung Ngoc Nguyen, Nguyen, Hung Ngoc, Hung P. Tong‐Viet +4 · 1 citation
Computer Science · Engineering · Mathematics · #20C15 (Primary) #20D05 (Secondary) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems #math.GR #math.RT #msc:20C15 #msc:20D05

paper · pdf · doi:10.48550/arxiv.1108.0010

26 pages

openalex publication_date 2011/07/29 · arxiv created 2015/01/30 · arxiv updated 2015/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≅ H× A for some abelian group A. In this paper, we confirm the conjecture for the family of projective special linear groups \textrmPSL₄(q) with q≥ 13.

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