A class of groups rich in finite quotients

If X is a class of groups, the class of counter-X groups is defined to consist of all groups having no non-trivial X-quotients. Counter-counter-finite groups are studied here; any non-trivial quotient of such a group has a non-trivial representation over any finitely generated domain, so we shall call these groups highly representable or HR-groups. Abelian, nilpotent, and solvable HR-groups are examined in detail, with structure theorems given in the abelian and nilpotent cases. Investigation of a subclass of solvable HR-groups leads to a generalization of Gruenberg's Theorem on the residual finiteness of finitely generated torsion-free nilpotent groups. Additional topics include characterizations of the HR radical and residual in groups with finite composition length, as well as the normal and subnormal structure of HR-groups.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Walter, Vonn Andrew

Contributors dc:contributor

• Robinson, Derek J.S.

• Mathematics

Statement dc:rights

• Copyright 1994 Walter, Vonn Andrew

Language dc:language

eng

Identifier

AAI9503344
(UMI)AAI9503344

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23456