{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/30383"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/30383","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"A measure for the number of commuting subgroups in compact groups","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Kazeem, Funmilayo Eniola"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Russo, Francesco G.","Kunzi, Hans-Peter Albert"],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019","date_published":"2019","updated_at":"2026-07-22T22:22:58Z","subjects":["Limits of probabilities","Profinite groups","Vietoris topology","Probability measures","Projective syste"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/30383","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Russo, Francesco G.","Kunzi, Hans-Peter Albert"]},{"key":"dc:creator","label":"Author","values":["Kazeem, Funmilayo Eniola"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-08-01T08:06:36Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-08-01T08:06:36Z"]},{"key":"dc:date.issued","label":"Date","values":["2019"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Limits of probabilities","Profinite groups","Vietoris topology","Probability measures","Projective syste"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/30383"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["A measure for the number of commuting subgroups in compact groups"]}]}],"canonical_facts":{"dc:contributor.advisor":["Russo, Francesco G.","Kunzi, Hans-Peter Albert"],"dc:creator":["Kazeem, Funmilayo Eniola"],"dc:date.accessioned":["2019-08-01T08:06:36Z"],"dc:date.available":["2019-08-01T08:06:36Z"],"dc:date.issued":["2019"],"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.uri":["http://hdl.handle.net/11427/30383"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["Limits of probabilities","Profinite groups","Vietoris topology","Probability measures","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"]},"updated_at":"2026-07-22T22:22:58Z"}