{"id":{"repo_id":"anu","oai_identifier":"oai:openresearch-repository.anu.edu.au:1885/133534"},"canonical_url":"https://search.dev.ndltd.org/etd/anu/oai:openresearch-repository.anu.edu.au:1885/133534","repository":{"repo_id":"anu","name":"Australian National University","base_url":"https://openresearch-repository.anu.edu.au/server/oai/request"},"display":{"title":"Locally finite near-fields","abstract":"A near-field is locally finite if every finite subset of it generates a finite sub-near-field. The main aim of this thesis is to give a coherent account of locally finite-near-fields, including finite ones. The well known results for finite near-fields are lised and proofs are given where appropriate. The results of Zassenhaus classify finite regular near-fields according to their order, pln, and the order of centres, pl, and Luneburg has determined the number of isomorphism types within each class. A polynomial h is given here which, together with the triple p, l, n, completely determines a finite regular near-field, up to isomorphism. The sub-near-field structure is determined in terms of these invariants and some results concerning near-field embeddings are included.","abstract_html":"A near-field is locally finite if every finite subset of it generates a finite sub-near-field. The main aim of this thesis is to give a coherent account of locally finite-near-fields, including finite ones. The well known results for finite near-fields are lised and proofs are given where appropriate. The results of Zassenhaus classify finite regular near-fields according to their order, pln, and the order of centres, pl, and Luneburg has determined the number of isomorphism types within each class. A polynomial h is given here which, together with the triple p, l, n, completely determines a finite regular near-field, up to isomorphism. The sub-near-field structure is determined in terms of these invariants and some results concerning near-field embeddings are included.","abstract_has_math":false,"creators":["Groves, Susan Dancs"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1974,"date_issued":"1974","date_published":"1974","updated_at":"2026-07-24T00:55:02Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["b1015840"],"render_values":[{"text":"b1015840","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1885/133534","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Groves, Susan Dancs"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-11-09T01:18:01Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-11-09T01:18:01Z"]},{"key":"dc:date.issued","label":"Date","values":["1974"]},{"key":"dc:type","label":"Dc Type","values":["Thesis (PhD)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["b1015840"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1885/133534"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A near-field is locally finite if every finite subset of it generates a finite sub-near-field. The main aim of this thesis is to give a coherent account of locally finite-near-fields, including finite ones. The well known results for finite near-fields are lised and proofs are given where appropriate. The results of Zassenhaus classify finite regular near-fields according to their order, pln, and the order of centres, pl, and Luneburg has determined the number of isomorphism types within each class. A polynomial h is given here which, together with the triple p, l, n, completely determines a finite regular near-field, up to isomorphism. The sub-near-field structure is determined in terms of these invariants and some results concerning near-field embeddings are included."]},{"key":"dc:title","label":"Title","values":["Locally finite near-fields"]}]}],"canonical_facts":{"dc:creator":["Groves, Susan Dancs"],"dc:date.accessioned":["2017-11-09T01:18:01Z"],"dc:date.available":["2017-11-09T01:18:01Z"],"dc:date.issued":["1974"],"dc:description.abstract":["A near-field is locally finite if every finite subset of it generates a finite sub-near-field. The main aim of this thesis is to give a coherent account of locally finite-near-fields, including finite ones. The well known results for finite near-fields are lised and proofs are given where appropriate. The results of Zassenhaus classify finite regular near-fields according to their order, pln, and the order of centres, pl, and Luneburg has determined the number of isomorphism types within each class. A polynomial h is given here which, together with the triple p, l, n, completely determines a finite regular near-field, up to isomorphism. The sub-near-field structure is determined in terms of these invariants and some results concerning near-field embeddings are included."],"dc:identifier.other":["b1015840"],"dc:identifier.uri":["http://hdl.handle.net/1885/133534"],"dc:language.iso":["en"],"dc:title":["Locally finite near-fields"],"dc:type":["Thesis (PhD)"]},"updated_at":"2026-07-24T00:55:02Z"}