\titleofpresentation{Centralizers in Locally Finite Groups}

\presenter{Pavel Shumyatsky}

It is well-known that centralizers play fundamental role in
the theory of locally finite groups. The main theme of our talk
will be the following question.

Let $G$ be a locally finite group admitting an automorphism $\phi$ of
finite order such that the centralizer $C_G(\phi)$ satisfies certain
finiteness conditions. What impact does this have on the structure of
the group $G$?

Sometimes the impact is quite strong and we will give
a survey of results illustrating this phenomena. In particular,
we concentrate on results where $G$ is shown to have a large nilpotent or
soluble subgroup. 

\presenteraddress{Department of Mathematics, University of Brasilia,
Brasilia-DF, 70910-900 Brazil }

\email{pavel@mat.unb.br}










