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Proceedings of the American Mathematical Society

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

 

 

A note on finite groups having a fixed-point-free automorphism


Author: Martin R. Pettet
Journal: Proc. Amer. Math. Soc. 52 (1975), 79-80
MSC: Primary 20D20
DOI: https://doi.org/10.1090/S0002-9939-1975-0404442-5
MathSciNet review: 0404442
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Abstract: A fusion result of Glauberman has as a consequence the fact that a finite group admitting a fixed-point-free automorphism has a normal Sylow $ 2$-subgroup (and in particular, is solvable) if all nontrivial fixed-point subgroups have odd order.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0404442-5
Keywords: Fixed-point-free automorphism, $ 2$-closed, $ Z(J(P))$ controls, strong fusion in $ P$
Article copyright: © Copyright 1975 American Mathematical Society