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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 | References | Similar Articles | Additional Information

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