
details
Title
Implicit characterization of radicals
Abstract By a Fitting pseudovariety we mean a class of finite groups which is
closed under taking quotients and subgroups and such that, in every
finite group, the product of normal subgroups which lie in the class
also lies in the class. The associated radical of a finite group is
the product of all normal subgroups which lie in the Fitting
pseudovariety. The problem we address is how the radical can be
described by some uniform formula which applies to all finite groups,
more precisely as the set of all parameter values which render
universally valid certain equations. For instance, a classical
theorem of Baer yields such a formula for the nilpotent radical, and
therefore for the pgroup radical. Although formulas have been
conjectured by Bandman et al, no such formulas are yet known for the
case of the solvable radical. The main of this talk is to introduce
these problems and a new approach to them which is part of ongoing
work with S. W. Margolis, B. Steinberg, and M. V. Volkov.
Speaker(s)
Jorge Almeida (CMUP / Matemática Pura, FCUP)
Date
June 06, 2006 Time 14:45 Room
Room 5.5

