Czechoslovak Mathematical Journal, online first, 8 pp.

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.

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

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 2010): 20C15, 20G40

DOI: 10.21136/CMJ.2017.0194-16

Full text available as PDF.


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