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dc.contributor.advisorO'Connor, John J. (John Joseph)
dc.contributor.authorBilgiç, Huseyin
dc.coverage.spatial147 p.en_US
dc.description.abstractIn this thesis, we analyse the structure of the centraliser of an element and of the normaliser of a cyclic subgroup in both Sn and An. We show that the centraliser in Sn of a permutation can be written as a direct product of centralisers of regular permutations and that the centraliser of a regular permutation is a wreath product. In certain cases we prove that this wreath product splits as a direct product and we analyse the centre of the subgroup. We calculate the centraliser of a general permutation in An and show how this is related to the centralisers of regular permutations. We investigate the normaliser of the cyclic subgroup generated by an element of Sn and show how this is related to the centraliser of the permutation. We calculate the centre of the normaliser and investigate when the normaliser splits as a direct product. We carry out a similar investigation for normalisers of cyclic subgroups of An and investigate the relationship between normalisers in An and Sn. We give presentations for both centralisers and normalisers.en_US
dc.publisherUniversity of St Andrewsen
dc.subject.lcshGroup theoryen
dc.titleCentralisers and normalisers in symmetric and alternating groupsen_US
dc.contributor.sponsorKahramanmaraş Sütçüimam Universityen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US

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