Czechoslovak Mathematical Journal, Vol. 67, No. 3, pp. 819-826, 2017


Characterizing projective general unitary groups ${\rm PGU}_3(q^2)$ by their complex group algebras

Farrokh Shirjian, Ali Iranmanesh

Received April 18, 2016.   First published August 10, 2017.

Abstract:  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.
Keywords:  character degree; complex group algebra; projective general unitary group
Classification MSC:  20C15, 20G40
DOI:  10.21136/CMJ.2017.0194-16


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Affiliations:   Farrokh Shirjian (corresponding author), Ali Iranmanesh, Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-137, Tehran, Iran, e-mail: fashirjian@gmail.com, Iranmanesh@modares.ac.ir

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