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Transactions of the American Mathematical Society

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

 

 

Hall-Higman type theorems. III


Author: T. R. Berger
Journal: Trans. Amer. Math. Soc. 228 (1977), 47-83
MSC: Primary 20C15
DOI: https://doi.org/10.1090/S0002-9947-1977-0437627-9
MathSciNet review: 0437627
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Abstract: This paper continues the investigations of this series. Suppose that $ G = ANS$ where S and NS are normal subgroups of G. Suppose that $ (\vert A\vert,\vert NS\vert) = 1$, S is extraspecial, and $ S/Z(S)$ is a faithful minimal module for the subgroup AN of G. Assume that k is a field of characteristic prime to $ \vert G\vert$ and V is a faithful irreducible $ {\mathbf{k}}[G]$-module. The structure of G is discussed in the minimal situation where N is cyclic, A is nilpotent, and $ V{\vert _A}$ does not have a regular A-direct summand.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0437627-9
Article copyright: © Copyright 1977 American Mathematical Society