Geodesic
Characterizing projective general unitary groups ${\rm PGU}_3(q^2)$ by their complex group algebras
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 819-826.

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Let $G$ be a finite group. Let $X_1(G)$ be the first column of the ordinary character table of $G$. We will show that if $X_1(G)=X_1({\rm PGU}_3(q^2))$, then $G \cong {\rm PGU}_3(q^2)$. As a consequence, we show that the projective general unitary groups ${\rm PGU}_3(q^2)$ are uniquely determined by the structure of their complex group algebras.
DOI : 10.21136/CMJ.2017.0194-16
Classification : 20C15, 20G40
Keywords: character degree; complex group algebra; projective general unitary group 
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     title = {Characterizing projective general unitary groups ${\rm PGU}_3(q^2)$ by their complex group algebras},
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Shirjian, Farrokh; Iranmanesh, Ali. Characterizing projective general unitary groups ${\rm PGU}_3(q^2)$ by their complex group algebras. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 819-826. doi : 10.21136/CMJ.2017.0194-16. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0194-16/

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