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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On linear groups over finite fields
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by Ji Ping Zhang
Proc. Amer. Math. Soc. 110 (1990), 53-57
DOI: https://doi.org/10.1090/S0002-9939-1990-1028297-1

Abstract:

Let $G$ be a finite group with an Abelian Sylow $p$-subgroup $P$ $(p > 5)$, and $F$, a finite field of characteristic $p$. Set $H = {O^{p’}}(G)$. If $G$ has a faithful FG-module $M$ such that ${\dim _F}M < p - 2$, then one of the following is true: (a) $P$ is normal in $G$, (b) $H/Z(H) \approx { \oplus _{i \leq t}}{L_2}({p^{{n_i}}})$, where ${n_i}$ and $t$ are positive integers and $2t < p - 2$, (c) $p = 7{\text {or}}11$ and $H \approx 2.{A_7}$ or ${J_1}$, respectively, ${\dim _F}M \geq p - 4$.
References
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Bibliographic Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 110 (1990), 53-57
  • MSC: Primary 20C20
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1028297-1
  • MathSciNet review: 1028297