## Computing with Matrix Groups (2001)

Venue: | GROUPS, COMBINATORICS AND GEOMETRY |

Citations: | 4 - 4 self |

### BibTeX

@ARTICLE{Kantor01computingwith,

author = {William M. Kantor and Ákos Seress},

title = {Computing with Matrix Groups},

journal = {GROUPS, COMBINATORICS AND GEOMETRY},

year = {2001},

pages = {123--137}

}

### OpenURL

### Abstract

A group is usually input into a computer by specifying the group either using a presentation or using a generating set of permutations or matrices. Here we will emphasize the latter approach, referring to [Si3, Si4, Ser1] for details of the other situations. Thus, the basic computational setting discussed here is as follows: a group is given, speciﬁed as G = X in terms of some generating set X of its elements, where X is an arbitrary subset of either Sn or GL(d, q ) (a familiar example is the group of Rubik’s cube). The goal is then to ﬁnd properties of G eﬃciently, such as |G|, the derived series, a composition series, Sylow subgroups, and so on.