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Derek J.S.Robinson Wu, Yu-Fen 2015-09-28T15:20:23Z 2015-09-28T15:20:23Z 10000-01-01 1998 1998 A group G is called a CT-group if commutativity is a transitive relation on the set of non-identity elements of G. This dissertation is concerned with the class of CT-groups. Finite and locally finite CT-groups are studied in detail with structure theorems given in both solvable and insolvable cases. The investigation of solvable CT-groups leads naturally to the study of fixed-point-free groups of automorphisms of abelian groups. Topics include a rank condition for the existence of fixed-point-free groups of automorphisms of abelian torsion groups, and the extensions of abelian groups by locally finite groups with fixed-point-free actions. Torsion-free solvable CT-groups and polycyclic CT-groups are also examined in detail with constructions and structure theorems. An additional topic studied is the subclass of groups in which all quotients of subgroups are CT. Made available in DSpace on 2015-09-28T15:20:23Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9904628.pdf: 2619459 bytes, checksum: 1506137bd26a4da6cf9441746c3dc3b1 (MD5) Previous issue date: 1998 Embargo set by: Seth Robbins for item 88245 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 64 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998. http://hdl.handle.net/2142/86964 (MiAaPQ)AAI9904628 eng Mathematics Groups in Which Commutativity Is a Transitive Relation text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.