A note on the Todd-Coxeter coset enumeration algorithm
نویسندگان
چکیده
منابع مشابه
On doing Todd-Coxeter enumeration in parallel*
Akl, S., G. Laborite, M. Leeder and K. Qiu, On doing Todd-Coxeter coset enumeration in parallel, Discrete Applied Mathematics 34 (1991) 27-35. The Todd-Coxeter coset enumeration method is without any doubt the best known and most used method in computational group theory. Surprisingly, however, it seems that no attempt has yet been made at producing a parallel version of it. This paper reports ...
متن کاملImplementation and Analysis of the Todd - Coxeter Algorithm
A recent form of the Todd-Coxeter algorithm, known as the lookahead algorithm, is described. The time and space requirements for this algorithm are shown experimentally to be usually either equivalent or superior to the Felsch and HaselgroveLeech-Trotter algorithms. Some findings from an experimental study of the behaviour of Todd-Coxeter programs in a variety of situations are given.
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 کاملConstructing Matrix Representations of Finitely Presented Groups
The Todd-Coxeter coset enumeration algorithm is one of the most powerful tools of computational group theory. It may be viewed as a means of constructing permutation representations of nitely presented groups. In this paper we present an analogous algorithm for directly constructing matrix representations over many elds. In fact the algorithm is more general than this, and can be used to constr...
متن کاملAndrews-Curtis and Todd-Coxeter proof words
Andrews and Curtis have conjectured that every balanced presentation of the trivial group can be transformed into a standard presentation by a finite sequence of elementary transformations. It can be difficult to determine whether or not the conjecture holds for a particular presentation. We show that the utility PEACE, which produces proofs based on Todd-Coxeter coset enumeration, can produce ...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1976
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500015790