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

## 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).

**final copy of Thesis of Charles Garnet Cox.pdf - Other**

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- Faculties (pre 2018 reorg) > Faculty of Social, Human and Mathematical Sciences (pre 2018 reorg) > Mathematical Sciences (pre 2018 reorg)

Current Faculties > Faculty of Social Sciences > School of Mathematical Sciences > Mathematical Sciences (pre 2018 reorg)

School of Mathematical Sciences > Mathematical Sciences (pre 2018 reorg)

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