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

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

2011-07-29

arxiv.org/abs/1108.0010v2

Mathematics

Group Theory

25 pages

Scientific paper

Let $G$ be a finite group and let $\cd(G)$ be the set of all 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 simple linear groups in dimension four.

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