Frobenius groups as groups of automorphisms
- Autores: N. Y. Makarenko, Pavel Shumyatsky
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 10, 2010, págs. 3425-3436
- Idioma: inglés
- DOI: 10.1090/s0002-9939-2010-10494-x
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Resumen
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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