Makarenko, N. Y. and Khukhro, E. I. and Shumyatsky, P.
(2011)
*Fixed points of Frobenius groups of automorphisms.*
Doklady Mathematics, 83
(2).
pp. 152-154.
ISSN 1064-5624

Full text not available from this repository.

Item Type: | Article |
---|---|

Item Status: | Live Archive |

## Abstract

A finite group admits a Frobenius automorphisms group FH with a kernel and complement H such that the fixed-point subgroup of F is trivial. It is further proved that every FH-invariant elementary Abelian section of G is a free module for an appropriate prime p. The exponent of a group is bounded with a metacyclic Frobenius group of automorphisms and it is supposed that a finite Frobenius group FH with cyclic kernel F and complement H acts on a finite group G. Bounds for the nilpotency class of groups and Lie rings admitting a metacyclic Frobenius group of automorphisms with fixed-point free kernel are obtained. It is also found that a locally nilpotent torsion-free group G admits a finite Frobenius group of automorphisms FH with cyclic kernel F and complement H of order q.

Additional Information: | Original Russian Text © N.Yu. Makarenko, E.I. Khukhro, P. Shumyatsky, 2011, published in Doklady Akademii Nauk, 2011, Vol. 437, No. 1, pp. 20–23. Presented by Academician Yu.L. Ershov August 2, 2010 |
---|---|

Keywords: | Algebra |

Subjects: | G Mathematical and Computer Sciences > G100 Mathematics |

Divisions: | College of Science > School of Mathematics and Physics |

Related URLs: | |

ID Code: | 15586 |

Deposited On: | 01 Jan 2016 19:43 |

Repository Staff Only: item control page