# Computers in group theory: a survey

@article{Cannon1969ComputersIG, title={Computers in group theory: a survey}, author={John J. Cannon}, journal={Commun. ACM}, year={1969}, volume={12}, pages={3-12} }

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…

## 32 Citations

### A survey of computer applications to semigroups and related structures

- MathematicsSIGS
- 1969

<u>Introducstion</u>. Although most of the applications of computers to abstract algebra have been made in group theory [4], there have been several applications to finite semigroups and related…

### Applications of coset enumeration

- Mathematics, Computer ScienceSYMSAC '71
- 1971

We describe here two applications of the Coxeter-Todd coset enumeration algorithm. One is the computation of part of the Schur multiplier of a small finite Lie group, in this case PSU(3, 4), directly…

### Computing irreducible representations of groups

- Mathematics
- 1970

How can you find a complete set of inequivalent irreducible (ordinary) representations of a finite group? The theory is classical but, except when the group was very small or had a rather special…

### Normalizers and centralizers of subgroups in non-Abelian groups of small order

- Mathematics
- 2012

Abstract. – By applying the computer program, which is created by authors, we obtain the exact representation of normalizers and centralizers of all nontrivial subgroups in non-Abelian groups under…

### Permutations Applied To Construction Company Management

- Mathematics
- 2013

groups Most groups considered in the first stage of the development of group theory were "concrete", having been realized through numbers, permutations, or matrices. It was not until the late…

### FORTRAN program for machine computation of group tables of finite groups

- Mathematics
- 1969

A FORTRAN program has been written for machine computation of group tables for finite groups and the use of the method depends on the fact that every finite group of order n is isomorphic to some subgroup of the symmetric group Sn.

### Computing Automorphisms of Finite Groups

- Mathematics
- 2006

In this thesis we explore the problem of computing automorphisms of finite groups, eventually focusing on some group product constructions. Roughly speaking, the automorphism group of a group gives…

### A general method to calculate all irreducible representations of a finite group

- Mathematics
- 1986

A so-called stochastic method is introduced which can be used to decompose the reducible representations of any finite group into irreducible representations. In this way, the regular representation…

### Use of computers in treating nonnumerical mathematics and group theoretical problems in physics

- MathematicsSIGS
- 1970

The main part of the paper forms a survey of algebraic and group theoretical programs used by or useful to physicists.

### Computing with Groups and Their Character Tables

- Mathematics
- 1982

In this survey an attempt is made to give some impression of the capabilities of currently available programs for computations with finitely generated groups and their representations.

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- Mathematics, Computer ScienceCanadian Mathematical Bulletin
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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.

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- Mathematics
- 1970

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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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p-groups may be classified by splitting the groups up into classes having the same commutator relations (isoclinism classes) and then determining the nonisomorphic groups in each class. This paper…

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This paper describes a practical procedure for computing the ordinary irreducible characters of finite groups (of orders up to 1000 or so). The novelty of the method consists of transposing the…