Computers in group theory: a survey

  title={Computers in group theory: a survey},
  author={John J. Cannon},
  journal={Commun. ACM},
Computers are being applied to an increasingly diverse range of problems in group theory. The most important areas of application at present are coset enumeration, sub-group lattices, automorphism groups of finite groups, character tables, and commutator calculus. Group theory programs range from simple combinatorial or numerical programs to large symbol manipulation systems. In this survey the more important algorithms in use are described and contrasted, and results which have been obtained… 

A survey of computer applications to semigroups and related structures

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A Machine Program for Coset Enumeration

  • H. Trotter
  • Mathematics, Computer Science
    Canadian Mathematical Bulletin
  • 1964
An algorithm for determining the index (when it is finite) of a subgroup H of a group K when K is specified by a finite set of generators and relations and H is specified as generated by a infinite set of words in the generators of K.

Coset enumeration on digital computers

  • J. Leech
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1963
In 1936 Todd and Coxeter gave a method ((10), also described in (4), ch. 2) for establishing the order of a finite group defined by a set of relations satisfied by its generators S1, S2,…, Sk. They

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