Experiments in coset enumeration

On the Efficiency of Some Finite Groups

“…A verification that {X | S} presents G relies on a successful coset enumeration [11]. A successful enumeration over the trivial subgroup gives a direct proof.…”

Proving a group trivial made easy: A case study in coset enumeration

“…The coset enumeration implementation which we used was ACE (advanced coset enumerator) by Havas and Ramsay [4], which is an enhanced version of the one described in [3]. The enumerations were performed on an SGI Origin 2000 computer which was equipped with enough memory to allow the definition of some hundreds of millions of cosets.…”

“…ACE has a mode whereby all the definitions are made using the HLT strategy, while definitions are tested against all essentially different positions after each individual coset/relator scan. Since our primary concern is to minimise the space requirements, this mixed strategy is the strategy we adopted; unless otherwise noted, it 108 G. Havas and C. Ramsay [4] was used for all the enumerations reported herein.…”

“…Apart from reordering the relators, it is well-known that rotating and inverting relators can also have a significant effect on performance (see Cannon, Dimino, Havas and Watson [1] and Havas and Ramsay [5]). We would expect this to be particularly effective for E2, given that the three relators in the presentation have many common subwords.…”

Computing with graphs and groups

“…Coset enumeration is one of the oldest and most useful methods of computational group theory (see [30,35,14] and their references). For this chapter, we concentrate on what coset enumeration does, and on the application of coset enumeration and related procedures to problems in graph theory.…”