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Robinson, Derek J.S. Walter, Vonn Andrew 2011-05-07T14:14:51Z 2011-05-07T14:14:51Z 10000-01-01 1994 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. Made available in DSpace on 2011-05-07T14:14:51Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9503344.pdf: 2321349 bytes, checksum: 9a7575b563e5508873b6958ea310c5eb (MD5) Previous issue date: 1994 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:04:36Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:30:53-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9503344 (UMI)AAI9503344 http://hdl.handle.net/2142/23456 eng Copyright 1994 Walter, Vonn Andrew Mathematics A class of groups rich in finite quotients text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.