Muhammad Sufi , Mohd Asri (2018) Residually finite properties of groups / Muhammad Sufi Mohd Asri. Masters thesis, University of Malaya.
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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.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | Dissertation (M.A.) – Faculty of Science, University of Malaya, 2018. |
| Uncontrolled Keywords: | Residually finite; weak potency; generalized free products; HNNExtensions; fundamental groups of graphs of groups |
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Divisions: | UNSPECIFIED |
| Depositing User: | Mr Mohd Safri Tahir |
| Date Deposited: | 19 Aug 2020 08:19 |
| Last Modified: | 19 Aug 2020 08:19 |
| URI: | http://studentsrepo.um.edu.my/id/eprint/10107 |
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