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On the topological entropy of nilpotent groups of finite rank
The present PhD thesis deals with some finiteness conditions on the topological entropy of continuous endomorphims of periodic locally compact Heisenberg p-groups (p prime). These are relevant models of locally compact nilpotent groups and their structure may be described very well by semidirect pro...
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| Format: | Thesis |
| Language: | English Eng |
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Department of Mathematics and Applied Mathematics
2025
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| _version_ | 1867613492014481408 |
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| access_status_str | Open Access |
| author | Waka, Olwethu |
| author2 | Russo, Francesco |
| author_browse | Russo, Francesco Waka, Olwethu |
| author_facet | Russo, Francesco Waka, Olwethu |
| author_sort | Waka, Olwethu |
| collection | Thesis |
| description | The present PhD thesis deals with some finiteness conditions on the topological entropy of continuous endomorphims of periodic locally compact Heisenberg p-groups (p prime). These are relevant models of locally compact nilpotent groups and their structure may be described very well by semidirect products. Firstly, we consider the class of locally compact abelian groups that are compactly generated; we recognize a relevant subclass among these, namely the slender groups, and observe that slender groups have very small values of topological entropy for their endomorphisms. Then we investigate a more general case of nilpotent periodic locally compact p-groups, reducing the computations to maximal p-subgroups. The role of p-groups becomes somehow fundamental, so we focus on locally compact Heisenberg p-groups which are studied especially on the field Qp of p-adic rationals and on the ring Zp of p-adic integers. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/41156 |
| institution | University of Cape Town (South Africa) |
| language | English Eng |
| last_indexed | 2026-06-10T12:37:00.307Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/41156 On the topological entropy of nilpotent groups of finite rank Waka, Olwethu Russo, Francesco Mathematics The present PhD thesis deals with some finiteness conditions on the topological entropy of continuous endomorphims of periodic locally compact Heisenberg p-groups (p prime). These are relevant models of locally compact nilpotent groups and their structure may be described very well by semidirect products. Firstly, we consider the class of locally compact abelian groups that are compactly generated; we recognize a relevant subclass among these, namely the slender groups, and observe that slender groups have very small values of topological entropy for their endomorphisms. Then we investigate a more general case of nilpotent periodic locally compact p-groups, reducing the computations to maximal p-subgroups. The role of p-groups becomes somehow fundamental, so we focus on locally compact Heisenberg p-groups which are studied especially on the field Qp of p-adic rationals and on the ring Zp of p-adic integers. 2025-03-12T09:10:43Z 2025-03-12T09:10:43Z 2024-05 2025-03-12T08:55:17Z Thesis / Dissertation Doctoral PhD http://hdl.handle.net/11427/41156 en Eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Waka, Olwethu On the topological entropy of nilpotent groups of finite rank |
| thesis_degree_str | Doctoral |
| title | On the topological entropy of nilpotent groups of finite rank |
| title_full | On the topological entropy of nilpotent groups of finite rank |
| title_fullStr | On the topological entropy of nilpotent groups of finite rank |
| title_full_unstemmed | On the topological entropy of nilpotent groups of finite rank |
| title_short | On the topological entropy of nilpotent groups of finite rank |
| title_sort | on the topological entropy of nilpotent groups of finite rank |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/41156 |
| work_keys_str_mv | AT wakaolwethu onthetopologicalentropyofnilpotentgroupsoffiniterank |