On the topological entropy of nilpotent groups of finite rank
| dc.contributor.advisor | Russo, Francesco | |
| dc.contributor.author | Waka, Olwethu | |
| dc.date.accessioned | 2025-03-12T09:10:43Z | |
| dc.date.available | 2025-03-12T09:10:43Z | |
| dc.date.issued | 2024-05 | |
| dc.date.updated | 2025-03-12T08:55:17Z | |
| dc.description.abstract | 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. | |
| dc.identifier.apacitation | Waka, O. (2024). <i>On the topological entropy of nilpotent groups of finite rank</i>. (). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/41156 | en_ZA |
| dc.identifier.chicagocitation | Waka, Olwethu. <i>"On the topological entropy of nilpotent groups of finite rank."</i> ., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2024. http://hdl.handle.net/11427/41156 | en_ZA |
| dc.identifier.citation | Waka, O. 2024. On the topological entropy of nilpotent groups of finite rank. . University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/41156 | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Waka, Olwethu AB - 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. DA - 2024-05 DB - OpenUCT DP - University of Cape Town KW - Mathematics LK - https://open.uct.ac.za PB - University of Cape Town PY - 2024 T1 - On the topological entropy of nilpotent groups of finite rank TI - On the topological entropy of nilpotent groups of finite rank UR - http://hdl.handle.net/11427/41156 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/41156 | |
| dc.identifier.vancouvercitation | Waka O. On the topological entropy of nilpotent groups of finite rank. []. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2024 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/41156 | en_ZA |
| dc.language.iso | en | |
| dc.language.rfc3066 | Eng | |
| dc.publisher.department | Department of Mathematics and Applied Mathematics | |
| dc.publisher.faculty | Faculty of Science | |
| dc.publisher.institution | University of Cape Town | |
| dc.subject | Mathematics | |
| dc.title | On the topological entropy of nilpotent groups of finite rank | |
| dc.type | Thesis / Dissertation | |
| dc.type.qualificationlevel | Doctoral | |
| dc.type.qualificationlevel | PhD |