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Transactions of the American Mathematical Society

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



Hall-Higman type theorems. II

Author: T. R. Berger
Journal: Trans. Amer. Math. Soc. 205 (1975), 47-69
MSC: Primary 20C05
MathSciNet review: 0399229
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Abstract: This paper continues the investigations of this series. Suppose $ {\mathbf{K}} =$   GF$ {\text{(}}r{\text{)}}$ is a field for a prime $ r;G$-is a nilpotent; $ V$ is a nonsingular symplectic space with form $ g$; and $ V$ is a faithful irreducible $ {\mathbf{K}}[G]$-module where $ G$ fixes the form $ g$. This paper describes completely the structure of $ G$ and its representation upon $ V$ when $ G$ is symplectic primitive. This latter condition is described in §4 and is a primitivity condition.

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Keywords: Hall-Higman Theorem B, representation theory, group theory, minimal module, symplectic primitive module
Article copyright: © Copyright 1975 American Mathematical Society

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