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Minimal generation of transitive permutation groups
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Tracey, Gareth M. (2017) Minimal generation of transitive permutation groups. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3140760~S15
Abstract
This thesis discusses upper bounds on the minimal number of elements d(G) required to generate a finite group G. We derive explicit upper bounds for the function d on transitive and minimally transitive permutation groups, in terms of their degree n. In the transitive case, bounds obtained first by Kovács and Newman, then by Bryant, Kovács and Robinson, and finally by Lucchini, Menegazzo and Morigi, show that d(G) = O(n/ √log n), for a transitive permutation group G of degree n. In this thesis, we find best possible estimates for the constant involved.
[Please consult thesis for remaining section of abstract.]
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Permutation groups, Finite groups | ||||
Official Date: | 4 May 2017 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Holt, Derek F. | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Format of File: | |||||
Extent: | vii, 101 leaves | ||||
Language: | eng |
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