Linear methods for studying automorphisms

Evgenii I. Khukhro,
Sobolev Institute of Mathematics of SB RAS, Novosibirsk, Russia

The study of automorphisms and their fixed points is one of the main research directions in the theory of groups. For solvable and nilpotent groups, it is natural to use the advantages of linear representations and methods related to Lie rings. In light of the classification of the finite simple groups, many problems that concern the automorphisms of finite groups are largely reduced to solvable and nilpotent groups.

List of topics:

  1. Automorphisms as linear transformations.
  2. The Clifford and Hall-Higman theorems.
  3. Restricting the nilpotency class.
  4. Powerful p-groups.
  5. Lie ring methods.
  6. Using Malcev and Lazard's correspondence.
  7. Generalized centralizer method.
  8. Excluding operators using nilpotency.