Giovanni De Franceschi, TU Kaiserslautern: Centralizers and conjugacy classes in finite classical groups

Referent: Giovanni De Franceschi: Centralizers and conjugacy classes in finite classical groups

Donnersta,  27.06.2019, 17:00 h

Ort:Raum 418-436

In computational group theory, solving problems on finite simple groups 
allows to solve problems in general, since there is plenty of literature
on how to extend solutions to extensions of groups and products of 
groups. Groups of matrices are one of the best known classes of finite 
simple groups, so studying classical groups (groups of isometries for 
non-degenerate forms on vector spaces) is the first step to get 
solutions of many problems. In this talk I show three strictly 
correlated problems: list conjugacy classes, describe explicitely a 
conjugacy element, describe the group structure of the centralizer of an
arbitrary element. During my PhD at University of Auckland I integrated
the pre-existing results for some particular cases and extended them to
subgroups of isometry groups (special and Omega groups). I will also 
show the results of the algorithmic study run parallel to the 
theoretical research.