RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Tr. Inst. Mat.: Year: Volume: Issue: Page: Find

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

On irreducible linear groups of prime-power degree

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 $C_G(A)/Z(\Gamma)\cong PSL(2,5)$.

Full text: PDF file (231 kB)
References: PDF file   HTML file
UDC: 512.542

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}