Finite groups and the fixed points of coprime automorphisms

Author:
Pavel Shumyatsky

Journal:
Proc. Amer. Math. Soc. **129** (2001), 3479-3484

MSC (1991):
Primary 20D45

DOI:
https://doi.org/10.1090/S0002-9939-01-06125-1

Published electronically:
April 25, 2001

MathSciNet review:
1860479

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a prime, and let be a finite -group acted on by an elementary abelian -group . The following results are proved:

1. If and is nilpotent of class at most for any , then the group is nilpotent of -bounded class.

2. If and is nilpotent of class at most for any , then the derived group is nilpotent of -bounded class.

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Additional Information

**Pavel Shumyatsky**

Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900 Brazil

Email:
pavel@ipe.mat.unb.br

DOI:
https://doi.org/10.1090/S0002-9939-01-06125-1

Keywords:
Automorphisms,
centralizers,
associated Lie rings

Received by editor(s):
April 26, 2000

Published electronically:
April 25, 2001

Additional Notes:
The author was supported by CNPq-Brazil

Communicated by:
Stephen D. Smith

Article copyright:
© Copyright 2001
American Mathematical Society