find a presentation for a subgroup of a group
pres( sg )
subgroup of a group given by generators and relations (i.e. a subgrel
Important: The group package has been deprecated. Use the superseding package GroupTheory instead.
This procedure attempts to find a set of relations among the given subgroup's generators sufficient to define the subgroup. The result is returned as a grelgroup.
The algorithm uses Todd-Coxeter coset enumeration, which is an inherently non-terminating process for infinite groups. Therefore, the algorithm will halt with an exception if too many cosets are generated during an attempt to enumerate cosets of a subgroup. The point at which the coset enumeration terminates is controlled by the environment variable _EnvMaxCosetsToddCoxeter, which has the default value 128000.
g ≔ grelgroup⁡a,b,c,d,a,b,c,1d,b,c,d,1a,c,d,a,1b,d,a,b,1c:
sg ≔ subgrel⁡x=a,b,y=a,c,g:
s ≔ subgrel⁡x=a,b,1a,grelgroup⁡a,b,a,a,a,b,b:
Error, (in group:-pres) too many cosets - subgroup may have infinite index; you can increase the coset limit by setting the environment variable _EnvMaxCosetsToddCoxeter to a value larger than 128000
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