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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. II


Author: Harvey I. Blau
Journal: Trans. Amer. Math. Soc. 203 (1975), 87-96
MSC: Primary 20C20
DOI: https://doi.org/10.1090/S0002-9947-1975-0379651-9
MathSciNet review: 0379651
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Abstract: Let $G$ be a finite group with a cyclic Sylow $p$-subgroup for some prime $p \geq 13$. Assume that $G$ is not of type ${L_2}(p)$, and that $G$ has a faithful indecomposable modular representation of degree $d \leq p$. Some known lower bounds for $d$ are improved, in case the center of the group is trivial, as a consequence of results on the degrees $\pmod p$ of irreducible Brauer characters in the principal $p$-block.


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Keywords: Indecomposable modular representation, small degree, cyclic Sylow <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$p$">-subgroup, main value
Article copyright: © Copyright 1975 American Mathematical Society