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Tr. Inst. Mat., 2012, Volume 20, Number 2, Pages 103–116 (Mi timb178)  

On irreducible linear groups of prime-power degree

A. A. Yadchenko

Gomel Branch Of Institute of Mathematics, National Academy of Sciences of Belarus

Abstract: Let $\Gamma=AG$ be a finite group, $G\triangleleft\Gamma$, $(|A|,|G|)=1$, $C_G(a)=C_G(A)$ for each element $a\in A^{#}$, and let the subgroup $A$ have a nonprimary odd order and be not normal in $\Gamma$. Assume that $\chi$ is an irreducible complex character of $G$ that is invariant for at least one nonunity element of $A$ and $\chi(1)<2|A|$. Then it is proved that $G=O_q(G)C_G(A)$ and $\chi(1)$ is a power of a prime $q$. Furthermore, if $G$ is not solvable, then $\chi(1)=2(|A|-1)$ and $C_G(A)/Z(\Gamma)\cong PSL(2,5)$.

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UDC: 512.542
Received: 03.12.2012

Citation: A. A. Yadchenko, “On irreducible linear groups of prime-power degree”, Tr. Inst. Mat., 20:2 (2012), 103–116

Citation in format AMSBIB
\Bibitem{Yad12}
\by A.~A.~Yadchenko
\paper On irreducible linear groups of prime-power degree
\jour Tr. Inst. Mat.
\yr 2012
\vol 20
\issue 2
\pages 103--116
\mathnet{http://mi.mathnet.ru/timb178}


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