A note on finite groups having a fixed-point-free automorphism
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- by Martin R. Pettet
- Proc. Amer. Math. Soc. 52 (1975), 79-80
- DOI: https://doi.org/10.1090/S0002-9939-1975-0404442-5
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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.References
- George Glauberman, A sufficient condition for $p$-stability, Proc. London Math. Soc. (3) 25 (1972), 253–287. MR 313383, DOI 10.1112/plms/s3-25.2.253
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- Elizabeth Wall Ralston, Solvability of finite groups admitting fixed-point-free automorphisms of order $rs$, J. Algebra 23 (1972), 164–180. MR 302759, DOI 10.1016/0021-8693(72)90053-1
- Benedetto Scimemi, Finite groups admitting a fixed-point-free automorphism, J. Algebra 10 (1968), 125–133. MR 229715, DOI 10.1016/0021-8693(68)90089-6
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- 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