Algebra, Logic and Topology

 

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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 p-group 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

 
     
 

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