Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-24T13:43:10.173Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Dade, E. C.. Carter subgroups and Fitting heights of finite solvable groups. Illinois J. Math. 13 (1969), 449–514.Google Scholar
[2]Espuelas, A.. The Fitting length of the Hughes subgroup. J. Algebra 105 (1987), 365–371.CrossRefGoogle Scholar
[3]Espuelas, A.. A noncoprime Shult type theorem. Math. Z., 196 (1987), 323–329.Google Scholar
[4]Isaacs, M.. Character Theory of Finite Groups (Academic Press, 1976).Google Scholar
[5]Shult, E.. On groups admitting fixed-point-free abelian operator groups. Illinois J. Math. 9 (1965), 701–720.Google Scholar
[6]Turull, A.. Supersolvable automorphism groups of solvable groups. Math. Z. 183 (1983), 47–73.Google Scholar