Khukhro, E. I.
(2012)
*Linear methods in the study of automorphisms.*
In: Algorithmic problems in group theory and related areas, July, 30 - August, 10, 2012, Chemal, Altai, Russia.

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## Abstract

Mainly about automorphisms of finite groups, but also some infinite (especially nilpotent). 1. Survey: Results on fixed-point-free and almost fixed-point-free automorphisms. Open problems 2. Some methods of representation theory: Automorphisms as linear transformations. Clifford's theorem. Hall--Higman--type theorems. Automorphism of prime order with fixed-point subgroup of given rank. 3. Lie ring methods: Automorphisms of Lie rings. Associated Lie rings. Method of graded centralizers. Automorphism of order $p$ acting on a finite $p$-group. Frobenius groups of automorphisms with fixed-point-free kernel. Lazard Lie algebra. 4. Baker--Campbell--Hausdorff formula: Mal'cev correspondence. Lazard correspondence. Automorphism of order $p^n$ acting on a finite $p$-group. 5. Elimination of operators by nilpotency.

Item Type: | Conference or Workshop Item (Lecture) |
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Uncontrolled Keywords: | Mainly about automorphisms of finite groups, but also some infinite (especially nilpotent). 1. Survey: Results on fixed-point-free and almost fixed-point-free automorphisms. Open problems 2. Some methods of representation theory: Automorphisms as linear transformations. Clifford's theorem. Hall--Higman--type theorems. Automorphism of prime order with fixed-point subgroup of given rank. 3. Lie ring methods: Automorphisms of Lie rings. Associated Lie rings. Method of graded centralizers. Automorphism of order $p$ acting on a finite $p$-group. Frobenius groups of automorphisms with fixed-point-free kernel. Lazard Lie algebra. 4. Baker--Campbell--Hausdorff formula: Mal'cev correspondence. Lazard correspondence. Automorphism of order $p^n$ acting on a finite $p$-group. 5. Elimination of operators by nilpotency. |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations |

Depositing User: | Professor Evgeny Khukhro |

Date Deposited: | 18 Oct 2012 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1890 |

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