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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Finite linear groups containing an irreducible solvable normal subgroup


Author: David L. Winter
Journal: Proc. Amer. Math. Soc. 25 (1970), 716
MSC: Primary 20.25
DOI: https://doi.org/10.1090/S0002-9939-1970-0258937-3
MathSciNet review: 0258937
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Abstract: The following theorem is proved. Let $G$ be a finite group which has a faithful representation $X$ of degree $n$ over the complex number field such that $X|H$ is irreducible where $H$ is a solvable normal subgroup of $G$. Let $p$ be a prime and assume that $n$ is neither a multiple of $p$ nor a multiple of a prime power ${q^s}$ with ${q^s} \equiv \pm 1\;\bmod \;p$. Then a $p$-Sylow subgroup of $G$ is normal and abelian.


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Keywords: Finite linear groups, irreducible normal solvable subgroup, normal abelian <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$p$">-Sylow subgroup
Article copyright: © Copyright 1970 American Mathematical Society