Speaker: Evgeny Khukhro (University of Lincoln & Sobolev Institute of Mathematics)
Date and time: October 29, 2020, 16:00 Novosibirsk time (UTC +7)
Abstract:
Bounding the
p-length or/and nilpotent length (Fitting height) of finite groups became a classical area of research since the seminal works of P. Hall and G. Higman of 1956 on Restricted Burnside Problem and of J. Thompson of 1964 on automorphisms. Various generalizations and improvements followed in a torrent of subsequent papers, mainly in the 1960s and 1970s. This area of research became somewhat less fashionable later, and a certain perception was even formed that nothing interesting remains to be discovered, that all the methods are already known. The purpose of my talk is to dispel this perception, to highlight several important open problems results about bounding the Fitting height and
p-length of finite soluble groups, as well as other length parameters applicable to not necessarily soluble groups. Among examples, there are problems about finite groups with
fixed-point-free and almost fixed-point-free automorphisms, about generalizations of the Restricted Burnside Problem, about coset identities, which have applications in the study of profinite groups, etc.
Chair: Evgeny Vdovin
Slides
Video