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Algorithms for subgroup presentations: computer implementation and applications
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dc.contributor.advisor | Robertson, E. F. | |
dc.contributor.author | Heggie, Patricia, M. | |
dc.coverage.spatial | 201 p. | en_US |
dc.date.accessioned | 2018-06-04T09:06:15Z | |
dc.date.available | 2018-06-04T09:06:15Z | |
dc.date.issued | 1991 | |
dc.identifier.uri | https://hdl.handle.net/10023/13684 | |
dc.description.abstract | One of the main algorithms of computational group theory is the Todd-Coxeter coset enumeration algorithm, which provides a systematic method for finding the index of a subgroup of a finitely presented group. This has been extended in various ways to provide not only the index of a subgroup, but also a presentation for the subgroup. These methods tie in with a technique introduced by Reidemeister in the 1920's and later improved by Schreier, now known as the Reidemeister-Schreier algorithm. In this thesis we discuss some of these variants of the Todd-Coxeter algorithm and their inter-relation, and also look at existing computer implementations of these different techniques. We then go on to describe a new package for coset methods which incorporates various types of coset enumeration, including modified Todd- Coxeter methods and the Reidemeister-Schreier process. This also has the capability of carrying out Tietze transformation simplification. Statistics obtained from running the new package on a collection of test examples are given, and the various techniques compared. Finally, we use these algorithms, both theoretically and as computer implementations, to investigate a particular class of finitely presented groups defined by the presentation: < a, b | aⁿ = b² = (ab-1) ß =1, ab² = ba²>. Some interesting results have been discovered about these groups for various values of β and n. For example, if n is odd, the groups turn out to be finite and metabelian, and if β= 3 or β= 4 the derived group has an order which is dependent on the values of n (mod 8) and n (mod 12) respectively. | en_US |
dc.language.iso | en | en_US |
dc.publisher | University of St Andrews | en |
dc.subject.lcc | QA171.C7H3 | |
dc.subject.lcsh | Group theory | en |
dc.title | Algorithms for subgroup presentations: computer implementation and applications | en_US |
dc.type | Thesis | en_US |
dc.contributor.sponsor | Science and Engineering Research Council (SERC) | en_US |
dc.type.qualificationlevel | Doctoral | en_US |
dc.type.qualificationname | PhD Doctor of Philosophy | en_US |
dc.publisher.institution | The University of St Andrews | en_US |
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