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Frobenius groups as groups of automorphisms
Author(s):
N.
Yu.
Makarenko;
Pavel
Shumyatsky
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3425-3436.
MSC (2010):
Primary 20D45, 17B70
Posted:
May 20, 2010
MathSciNet review:
2661543
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Abstract:
We show that if  is a double Frobenius group with ``upper'' complement  of order  such that  is nilpotent of class  , then  is nilpotent of  -bounded class. This solves a problem posed by Mazurov in the Kourovka Notebook. The proof is based on an analogous result on Lie rings: if a finite Frobenius group  with kernel  of prime order and complement  of order  acts on a Lie ring  in such a way that  and  is nilpotent of class  , then  is nilpotent of  -bounded class.
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Additional Information:
N.
Yu.
Makarenko
Affiliation:
Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
Address at time of publication:
Laboratoire de Mathématiques, Informatique et Application, Université de Haute Alsace, Mulhouse, 68093, France
Email:
natalia_makarenko@yahoo.fr
Pavel
Shumyatsky
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900, Brazil
Email:
pavel@mat.unb.br
DOI:
10.1090/S0002-9939-2010-10494-X
PII:
S 0002-9939(2010)10494-X
Keywords:
Automorphisms,
centralizers,
associated Lie rings
Received by editor(s):
November 13, 2009
Posted:
May 20, 2010
Additional Notes:
The first author was supported in part by the Programme of Support of Leading Scientific Schools of the Russian Federation.
The second author was supported by CNPq-Brazil.
Communicated by:
Jonathan I. Hall
Copyright of article:
Copyright
2010,
American Mathematical Society
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