GENERAL
SEMINAR

“On noncoprime fixed point
free

action”

by

GÜLİN
ERCAN

METU

Abstract: Let G be a _nite group and A be a group of automorphisms of G. The structure of the _xed
point subgroup CG(A) = fg 2 Gjga = g for all a 2 Ag of A in G and the way it is embedded in G have been found to be very
infor-mative about the structure of G. Problems of this type are studied by many mathematicians
under the assumption that jGj and jAj are relatively prime. There exist certain very useful
relations between the groups G and A which facilitate the applications of some inductive
arguments. In the case of a nonco-prime action it less so. It is conjectured
that the Fitting length of G is bounded above by the number of primes dividing the order
of A when G is solvable, A is nilpotent and CG(A) =
1, in other words A acts _xed point freely on G. The aim of this seminar is to present recent
contributions to this problem.

Date : October 27, 2010 (Wednesday)

Time : 15.40

Place: Bilkent University ,Mathematics Seminar Room SA141

Tea will be served before the seminar.