Redfern, Ian Douglas (1993) Automatic coset systems. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Library of Congress Subject Headings (LCSH):	Algorithms, Computer science -- Mathematics, Geometry
Official Date:	September 1993
Dates:	Date Event September 1993 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Holt, Derek
Sponsors:	Science and Engineering Research Council (Great Britain) (SERC)
Extent:	iii, 61, [c.40] leaves : illustrations
Language:	eng

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