A measure for the number of commuting subgroups in compact groups
| dc.contributor.advisor | Russo, Francesco G. | |
| dc.contributor.advisor | Kunzi, Hans-Peter Albert | |
| dc.contributor.author | Kazeem, Funmilayo Eniola | |
| dc.date.accessioned | 2019-08-01T08:06:36Z | |
| dc.date.available | 2019-08-01T08:06:36Z | |
| dc.date.issued | 2019 | |
| dc.date.updated | 2019-07-31T08:31:49Z | |
| dc.description.abstract | 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. | |
| dc.identifier.apacitation | Kazeem, F. E. (2019). <i>A measure for the number of commuting subgroups in compact groups</i>. (). ,Faculty of Science ,Department of Maths & Applied Maths. Retrieved from http://hdl.handle.net/11427/30383 | en_ZA |
| dc.identifier.chicagocitation | Kazeem, Funmilayo Eniola. <i>"A measure for the number of commuting subgroups in compact groups."</i> ., ,Faculty of Science ,Department of Maths & Applied Maths, 2019. http://hdl.handle.net/11427/30383 | en_ZA |
| dc.identifier.citation | Kazeem, F.E. 2019. A measure for the number of commuting subgroups in compact groups. . ,Faculty of Science ,Department of Maths & Applied Maths. http://hdl.handle.net/11427/30383 | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Kazeem, Funmilayo Eniola AB - 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. DA - 2019 DB - OpenUCT DP - University of Cape Town KW - Limits of probabilities KW - Profinite groups KW - Vietoris topology KW - Probability measures KW - Projective syste LK - https://open.uct.ac.za PY - 2019 T1 - A measure for the number of commuting subgroups in compact groups TI - A measure for the number of commuting subgroups in compact groups UR - http://hdl.handle.net/11427/30383 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/30383 | |
| dc.identifier.vancouvercitation | Kazeem FE. A measure for the number of commuting subgroups in compact groups. []. ,Faculty of Science ,Department of Maths & Applied Maths, 2019 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/30383 | en_ZA |
| dc.language.rfc3066 | Eng | |
| dc.publisher.department | Department of Mathematics and Applied Mathematics | |
| dc.publisher.faculty | Faculty of Science | |
| dc.subject | Limits of probabilities | |
| dc.subject | Profinite groups | |
| dc.subject | Vietoris topology | |
| dc.subject | Probability measures | |
| dc.subject | Projective syste | |
| dc.title | A measure for the number of commuting subgroups in compact groups | |
| dc.type | Doctoral Thesis | |
| dc.type.qualificationlevel | Doctoral | |
| dc.type.qualificationname | PhD |