Files in this item



application/pdf9904628.pdf (3MB)Restricted to U of Illinois
(no description provided)PDF


Title:Groups in Which Commutativity Is a Transitive Relation
Author(s):Wu, Yu-Fen
Doctoral Committee Chair(s):Derek J.S.Robinson
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Abstract: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.
Issue Date:1998
Description:64 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998.
Other Identifier(s):(MiAaPQ)AAI9904628
Date Available in IDEALS:2015-09-28
Date Deposited:1998

This item appears in the following Collection(s)

Item Statistics