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A measure for the number of commuting subgroups in compact groups
The present thesis is devoted to the construction of a probability measure which counts the pairs of closed commuting subgroups in infinite groups. This measure turns out to be an extension of what was known in the finite case as subgroup commutativity degree and opens a new approach of study for th...
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| Format: | Thesis |
| Language: | Eng |
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Department of Mathematics and Applied Mathematics
2019
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| _version_ | 1867613224456683520 |
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| access_status_str | Open Access |
| author | Kazeem, Funmilayo Eniola |
| author2 | Russo, Francesco G. |
| author_browse | Kazeem, Funmilayo Eniola Russo, Francesco G. |
| author_facet | Russo, Francesco G. Kazeem, Funmilayo Eniola |
| author_sort | Kazeem, Funmilayo Eniola |
| collection | Thesis |
| description | The present thesis is devoted to the construction of a probability measure which counts the pairs of closed commuting subgroups in infinite groups. This measure turns out to be an extension of what was known in the finite case as subgroup commutativity degree and opens a new approach of study for the class of near abelian groups, recently introduced in [24, 27]. The extremal case of probability one characterises the topologically quasihamiltonian groups, studied originally by K. Iwasawa [30, 31] in the abstract case and then by F. K¨ummich [35, 36, 37], C. Scheiderer [45, 46], P. Diaconis [11] and S. Strunkov [48] in the topological case. Our probability measure turns out to be a useful tool in describing the distance of a profinite group from being topologically quasihamiltonian. We have been inspired by an idea of H. Heyer in the present context of investigation and in fact we generalise some of his techniques, in order to construct a probability measure on the space of closed subgroups of a profinite group. This has been possible because the space of closed subgroups of a profinite group may be approximated by finite spaces and the consequence is that our probability measure may be approximated by finite probability measures. While we have a satisfactory description for profinite groups and compact groups, the case of locally compact groups remains open in its generality. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/30383 |
| institution | University of Cape Town (South Africa) |
| language | Eng |
| last_indexed | 2026-06-10T12:32:44.899Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| 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:11427/30383 A measure for the number of commuting subgroups in compact groups Kazeem, Funmilayo Eniola Russo, Francesco G. Kunzi, Hans-Peter Albert Limits of probabilities Profinite groups Vietoris topology Probability measures Projective syste The present thesis is devoted to the construction of a probability measure which counts the pairs of closed commuting subgroups in infinite groups. This measure turns out to be an extension of what was known in the finite case as subgroup commutativity degree and opens a new approach of study for the class of near abelian groups, recently introduced in [24, 27]. The extremal case of probability one characterises the topologically quasihamiltonian groups, studied originally by K. Iwasawa [30, 31] in the abstract case and then by F. K¨ummich [35, 36, 37], C. Scheiderer [45, 46], P. Diaconis [11] and S. Strunkov [48] in the topological case. Our probability measure turns out to be a useful tool in describing the distance of a profinite group from being topologically quasihamiltonian. We have been inspired by an idea of H. Heyer in the present context of investigation and in fact we generalise some of his techniques, in order to construct a probability measure on the space of closed subgroups of a profinite group. This has been possible because the space of closed subgroups of a profinite group may be approximated by finite spaces and the consequence is that our probability measure may be approximated by finite probability measures. While we have a satisfactory description for profinite groups and compact groups, the case of locally compact groups remains open in its generality. 2019-08-01T08:06:36Z 2019-08-01T08:06:36Z 2019 2019-07-31T08:31:49Z Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/30383 Eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Limits of probabilities Profinite groups Vietoris topology Probability measures Projective syste Kazeem, Funmilayo Eniola A measure for the number of commuting subgroups in compact groups |
| thesis_degree_str | Doctoral |
| title | A measure for the number of commuting subgroups in compact groups |
| title_full | A measure for the number of commuting subgroups in compact groups |
| title_fullStr | A measure for the number of commuting subgroups in compact groups |
| title_full_unstemmed | A measure for the number of commuting subgroups in compact groups |
| title_short | A measure for the number of commuting subgroups in compact groups |
| title_sort | measure for the number of commuting subgroups in compact groups |
| topic | Limits of probabilities Profinite groups Vietoris topology Probability measures Projective syste |
| url | http://hdl.handle.net/11427/30383 |
| work_keys_str_mv | AT kazeemfunmilayoeniola ameasureforthenumberofcommutingsubgroupsincompactgroups AT kazeemfunmilayoeniola measureforthenumberofcommutingsubgroupsincompactgroups |