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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\vert 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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DOI: https://doi.org/10.1090/S0002-9939-1970-0258937-3
Keywords: Finite linear groups, irreducible normal solvable subgroup, normal abelian $ p$-Sylow subgroup
Article copyright: © Copyright 1970 American Mathematical Society