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- Todd–Coxeter_algorithm abstract "In group theory, the Todd–Coxeter algorithm, created by J. A. Todd and H. S. M. Coxeter in 1936, is an algorithm for solving the coset enumeration problem. Given a presentation of a group G by generators and relations and a subgroup H of G, the algorithm enumerates the cosets of H on G and describes the permutation representation of G on the space of the cosets. If the order of a group G is relatively small and the subgroup H is known to be uncomplicated (for example, a cyclic group), then the algorithm can be carried out by hand and gives a reasonable description of the group G. Using their algorithm, Coxeter and Todd showed that certain systems of relations between generators of known groups are complete, i.e. constitute systems of defining relations.The Todd–Coxeter algorithm can be applied to infinite groups and is known to terminate in a finite number of steps, provided that the index of H in G is finite. On the other hand, for a general pair consisting of a group presentation and a subgroup, its running time is not bounded by any computable function of the index of the subgroup and the size of the input data.".
- Todd–Coxeter_algorithm wikiPageID "894779".
- Todd–Coxeter_algorithm wikiPageRevisionID "580992005".
- Todd–Coxeter_algorithm subject Category:Computational_group_theory.
- Todd–Coxeter_algorithm comment "In group theory, the Todd–Coxeter algorithm, created by J. A. Todd and H. S. M. Coxeter in 1936, is an algorithm for solving the coset enumeration problem. Given a presentation of a group G by generators and relations and a subgroup H of G, the algorithm enumerates the cosets of H on G and describes the permutation representation of G on the space of the cosets.".
- Todd–Coxeter_algorithm label "Algorithme de Todd-Coxeter".
- Todd–Coxeter_algorithm label "Todd-Coxeter-Algorithmus".
- Todd–Coxeter_algorithm label "Todd-Coxeter-algoritme".
- Todd–Coxeter_algorithm label "Todd–Coxeter algorithm".
- Todd–Coxeter_algorithm label "Алгоритм Тодда — Коксетера".
- Todd–Coxeter_algorithm sameAs Todd%E2%80%93Coxeter_algorithm.
- Todd–Coxeter_algorithm sameAs Todd-Coxeter-Algorithmus.
- Todd–Coxeter_algorithm sameAs Algorithme_de_Todd-Coxeter.
- Todd–Coxeter_algorithm sameAs Todd-Coxeter-algoritme.
- Todd–Coxeter_algorithm sameAs Q690505.
- Todd–Coxeter_algorithm sameAs Q690505.
- Todd–Coxeter_algorithm wasDerivedFrom Todd–Coxeter_algorithm?oldid=580992005.