Locally finite near-fields
type: CreativeWork
description: 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: 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.
author: Groves, Susan Dancs
language: en
date published: 1974
date modified: 2026-07-24T01:07:45Z
provider: Australian Catholic University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Australian Catholic University

PropertyValue
property ID: Handle
value: http://hdl.handle.net/1885/133534