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arXiv · 1108.0010

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
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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 $q\geq 13$.

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Hung Ngoc Nguyen, Hung P. Tong-Viet, Thomas P. Wakefield. 2011-07-29. Projective special linear groups $PSL_4(q)$ are determined by the set of their character degrees. https://arxiv.org/abs/1108.0010

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