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On fixed-point-free elements

Published online by Cambridge University Press:  24 October 2008

Alberto Espuelas
Alberto Espuelas
Affiliation:
Departamento de Algebra, Universidad de Zaragoza, Zaragoza, Spain
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Extract

In Theorem 1·2 of [3] the following extension of the classical theorem of Shult is proved.

Theorem. Let G be a p-solvable group and let V be a faithful KG-module, where char. Assume that G contains an element x of order pn acting fixed-pointfreely on V. If p is a Fermat prime suppose further that the Sylow 2-subgroups of G are abelian. If p = 2 assume that the Sylow q-subgroups of G for each Mersenne prime q less than 2n are abelian. Then

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 207 - 211
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Dade, E. C.. Carter subgroups and Fitting heights of finite solvable groups. Illinois J. Math. 13 (1969), 449–514.Google Scholar
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