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Title: Automatic coset systems
Author: Redfern, Ian Douglas
ISNI:       0000 0001 3510 7076
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1993
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This thesis describes the theory of automatic coset systems. These provide a simple and economical way of describing a system of co- sets in a group with respect to a subgroup, such as the cosets of the stabiliser of an object under a group of transformations. An automatic coset system possesses a finite state automaton that provides a name for each coset, and a set of finite state automata that allow these cosets to be multiplied by group generators. An algorithm is given that will produce a certain type of automatic coset system, should one exist, from a description of the group and subgroup. The type of system produced has the advantage that it names each coset uniquely using as short a name as possible. This makes it particularly useful for coset enumeration, and several ex- amples of its use are given in an appendix. Two theorems are also proved: the property of being an automatic coset system is independent of the generating set chosen, and quasiconvex subgroups of hyperbolic groups have automatic coset sys- tems.
Supervisor: Not available Sponsor: Science and Engineering Research Council (Great Britain) (SERC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics ; QA76 Electronic computers. Computer science. Computer software