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Title: The cyclizer series of infinite permutation groups
Author: Turner, Simon
ISNI:       0000 0004 2740 8372
Awarding Body: University of Bath
Current Institution: University of Bath
Date of Award: 2013
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The cyclizer of an infinite permutation group G is the group generated by the cycles involved in elements of G, along with G itself. There is an ascending subgroup series beginning with G, where each term in the series is the cyclizer of the previous term. We call this series the cyclizer series for G. If this series terminates then we say the cyclizer length of G is the length of the respective cyclizer series. We study several innite permutation groups, and either determine their cyclizer series, or determine that the cyclizer series terminates and give the cyclizer length. In each of the innite permutation groups studied, the cyclizer length is at most 3. We also study the structure of a group that arises as the cyclizer of the innite cyclic group acting regularly on itself. Our study discovers an interesting innite simple group, and a family of associated innite characteristically simple groups.
Supervisor: Smith, Geoffrey Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available