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Infinite permutation groups containing all finitary permutations

Infinite permutation groups containing all finitary permutations
Infinite permutation groups containing all finitary permutations
Groups naturally occu as the symmetries of an object. This is why they appear in so many different areas of mathematics. For example we find class grops in number theory, fundamental groups in topology, and amenable groups in analysis. In this thesis we will use techniques and approaches from various fields in order to study groups.

This is a 'three paper' thesis, meaning that the main body of the document is made up of three papers. The first two of these look at permutation groups which contain all permutations with finite support, the first focussing on decision problems and the second on the R? property (which involves counting the number of twisting conjugacy classes in a group). The third works with wreath products C}Z where C is cyclic, and looks to dermine the probability of choosing two elements in a group which commute (known as the degree of commutativity, a topic which has been studied for finite groups intensely but at the time of writing this thesis has only two papers involving infinite groups, one of which is in this thesis).
Cox, Charles
522d9ea0-0890-41c6-848a-bcd0a45e2fca
Cox, Charles
522d9ea0-0890-41c6-848a-bcd0a45e2fca
Martino, Armando
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Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944

(2016) Infinite permutation groups containing all finitary permutations. University of Southampton, School of Mathematics, Doctoral Thesis, 124pp.

Record type: Thesis (Doctoral)

Abstract

Groups naturally occu as the symmetries of an object. This is why they appear in so many different areas of mathematics. For example we find class grops in number theory, fundamental groups in topology, and amenable groups in analysis. In this thesis we will use techniques and approaches from various fields in order to study groups.

This is a 'three paper' thesis, meaning that the main body of the document is made up of three papers. The first two of these look at permutation groups which contain all permutations with finite support, the first focussing on decision problems and the second on the R? property (which involves counting the number of twisting conjugacy classes in a group). The third works with wreath products C}Z where C is cyclic, and looks to dermine the probability of choosing two elements in a group which commute (known as the degree of commutativity, a topic which has been studied for finite groups intensely but at the time of writing this thesis has only two papers involving infinite groups, one of which is in this thesis).

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More information

Published date: August 2016
Organisations: University of Southampton, Mathematical Sciences

Identifiers

Local EPrints ID: 401538
URI: http://eprints.soton.ac.uk/id/eprint/401538
PURE UUID: 843bc172-e4a6-46ec-8d06-667dd00cadb5
ORCID for Armando Martino: ORCID iD orcid.org/0000-0002-5350-3029
ORCID for Graham Niblo: ORCID iD orcid.org/0000-0003-0648-7027

Catalogue record

Date deposited: 27 Oct 2016 13:08
Last modified: 13 Jun 2019 00:39

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