subgrel - Help

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subgrel

represent a subgroup of a group

 Calling Sequence subgrel(gens, grelgrp)

Parameters

 gens - set of equations designating the generators of the subgroup grelgrp - the group for which this is a subgroup

Description

 • The function subgrel is used as a procedure and an unevaluated procedure call. As a procedure, subgrel checks its arguments and then either exits with an error or returns the unevaluated subgrel call.
 • The first argument is a set of equations or words on the generators of the parent group. The left side of each equation is the name of a subgroup generator; the right side is a word in the group generators (see grelgroup) representing the subgroup generator. If only a word is specified, then a name for the generator is produced automatically.

Examples

 > $\mathrm{subgrel}\left(\left\{x=\left[a,b,\frac{1}{a}\right]\right\},\mathrm{grelgroup}\left(\left\{a,b\right\},\left\{\left[a,a,a\right],\left[b,b\right]\right\}\right)\right)$
 ${\mathrm{subgrel}}{}\left(\left\{{x}{=}\left[{a}{,}{b}{,}\frac{{1}}{{a}}\right]\right\}{,}{\mathrm{grelgroup}}{}\left(\left\{{a}{,}{b}\right\}{,}\left\{\left[{b}{,}{b}\right]{,}\left[{a}{,}{a}{,}{a}\right]\right\}\right)\right)$ (1)

the next example will give an error:

 > $\mathrm{subgrel}\left(\left\{y=\left[a,b,c\right]\right\},\mathrm{grelgroup}\left(\left\{a,b\right\},\left\{\left[a,a\right],\left[b,a\right]\right\}\right)\right)$

Maple will generate names for any unnamed generators:

 > $\mathrm{subgrel}\left(\left\{\left[a,a,a\right],u=\left[b,b\right]\right\},\mathrm{grelgroup}\left(\left\{a,b\right\},\left\{\left[a,b,\frac{1}{a},\frac{1}{b}\right]\right\}\right)\right)$
 ${\mathrm{subgrel}}{}\left(\left\{{\mathrm{_x}}{=}\left[{a}{,}{a}{,}{a}\right]{,}{u}{=}\left[{b}{,}{b}\right]\right\}{,}{\mathrm{grelgroup}}{}\left(\left\{{a}{,}{b}\right\}{,}\left\{\left[{a}{,}{b}{,}\frac{{1}}{{a}}{,}\frac{{1}}{{b}}\right]\right\}\right)\right)$ (2)

 See Also

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