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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
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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Keywords: Fixed-point-free automorphism, <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$2$">-closed, <IMG WIDTH="80" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$Z(J(P))$"> controls, strong fusion in <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img5.gif" ALT="$P$">
Article copyright: © Copyright 1975 American Mathematical Society