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Proceedings of the American Mathematical Society

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

 
 

 

Some criteria for the nonexistence of certain finite linear groups


Author: Harvey I. Blau
Journal: Proc. Amer. Math. Soc. 43 (1974), 283-286
MSC: Primary 20C20
DOI: https://doi.org/10.1090/S0002-9939-1974-0332946-1
MathSciNet review: 0332946
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Abstract: Let $ p$ be a prime and $ G$ a finite group, not of type $ {L_2}(p)$, with a cyclic Sylow $ p$-subgroup $ P$. Assume that $ G = G'$. The purpose of this note is to put some rather stringent lower bounds on the degree $ d$ of a faithful indecomposable representation of $ G$ over a field of characteristic $ p$ given certain conditions on the normalizer $ N$ and the centralizer $ C$ of $ P$ in $ G$. In particular, if the center of $ G$ has order 2 and $ \vert N:C\vert = p - 1$, then $ d \geqq p - 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0332946-1
Keywords: Indecomposable modular representation, small degree, cyclic Sylow $ p$-subgroup
Article copyright: © Copyright 1974 American Mathematical Society

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