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A class of groups rich in finite quotients

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Title: A class of groups rich in finite quotients
Author(s): Walter, Vonn Andrew
Doctoral Committee Chair(s): Robinson, Derek J.S.
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Mathematics
Abstract: 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.
Issue Date: 1994
Type: Text
Language: English
Rights Information: Copyright 1994 Walter, Vonn Andrew
Date Available in IDEALS: 2011-05-07
Identifier in Online Catalog: AAI9503344
OCLC Identifier: (UMI)AAI9503344

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