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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Under the degree of some finite linear groups

Author: Harvey I. Blau
Journal: Trans. Amer. Math. Soc. 155 (1971), 95-113
MSC: Primary 20.80
Erratum: Trans. Amer. Math. Soc. 162 (1971), 475.
MathSciNet review: 0274604
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Abstract: Let $ G$ be a finite group with a cyclic Sylow $ p$-subgroup $ P$ for some prime $ p \geqq 13$. Assume that $ G$ is not of type $ {L_2}(p)$, and that $ G$ has a faithful indecomposable modular representation of degree $ d \leqq p$. This paper offers several improvements of the known bound $ d \geqq (7p)/10 - 1/2$. In particular, $ d \geqq 3(p - 1)/4$. Other bounds are given relative to the order of the center of $ G$ and the index of the centralizer of $ P$ in its normalizer.

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Keywords: Indecomposable modular representation, small degree, cyclic Sylow $ p$-subgroup, symmetric decomposition, skew decomposition, irreducible complex representation
Article copyright: © Copyright 1971 American Mathematical Society