Date of Award

12-1-2018

Thesis Type

masters

Document Type

Thesis (Restricted Access)

Department

Faculty of Science

Institution

University of Malaya

Abstract

In this thesis, we shall study two stronger forms of residual finiteness, namely cyclic subgroup separability and weak potency in various generalized free products and HNN extensions. Among our results, we shall show that the generalized free products and HNN extensions where the amalgamated or associated subgroups are finite, or central, or infinite cyclic, or they are direct products of an infinite cyclic subgroup with a finite subgroup, or they are finite extensions of central subgroups, are again cyclic subgroup separable or weakly potent respectively. In order to prove our results, we shall prove a criterion each for the weak potency of generalized free products and HNN extensions, but we shall use previously established criterions for cyclic subgroup separability. Finally, we shall extend our results to tree products and fundamental groups of graphs of groups.

Note

Dissertation (M.A.) – Faculty of Science, University of Malaya, 2018.

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