منابع مشابه
Double-coset enumeration algorithm for symmetrically generated groups
The Todd-Coxeter algorithm described in [13] remains a primary reference for coset enumeration programs. It may be viewed as a means of constructing permutation representations of finitely presented groups. A number of effective computer programs for singlecoset enumeration have been described, see, for example, [2, 7, 8]. Enumerating double cosets, rather than single cosets, gives substantial ...
متن کاملExperiments in Coset Enumeration
Coset enumeration, based on the methods described by Todd and Coxeter, is one of the most important tools for investigating nitely presented groups. Such methods do not, in general, constitute an algorithm. Each problem has to be addressed individually, and determining whether or not an acceptable solution for a diicult problem can be found using given resources requires an empirical approach (...
متن کاملObservations on Coset Enumeration
Todd and Coxeter's method for enumerating cosets of nitely generated subgroups in nitely presented groups (abbreviated by Tc here) is one famous method from combinatorial group theory for studying the subgroup problem. Since preex string rewriting is also an appropriate method to study this problem, preex string rewriting methods have been compared to Tc. We recall and compare two of them briee...
متن کاملParallel Coset Enumeration Using Threads
Coset enumeration is one of the basic tools for investigating nitely presented groups. Many enumerations require signiicant resources, in terms of CPU time or memory space. We develop a fully functional parallel coset enumeration procedure and we discuss some of the issues involved in such parallelisation using the POSIX threads library. Our results can equally well be applied to any master-sla...
متن کاملMSc project: Coset enumeration and its applications
This project is appropriate for someone with an interest in both group theory and algorithms. Familiarity with basic group theory is essential. A group may be described very compactly via a presentation by generators and relations. For example, the alternating group A5 of order 60 is isomorphic to 〈x, y | x = y = (xy) = 1〉. However, it is not usually easy to study a group given by a presentatio...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1991
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(08)80094-6