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group(deprecated)

 permrep
 find a permutation representation of a group

 Calling Sequence permrep(sbgrl)

Parameters

 sbgrl - subgroup of a group given by generators and relations (i.e. a subgrel)

Description

 • Important: The group package has been deprecated. Use the superseding command GroupTheory[PermutationGroup] instead.
 • This function finds all the right cosets of the given subgroup in the given group, assigns integers consecutively to these cosets, constructs a permutation on these coset numbers for each group generator, and returns the permutation group generated by these permutations. Thus the permutation group will be a homomorphic image of (but not necessarily isomorphic to) the original group. A permgroup is returned whose generators are named the same as the original group generators.
 • The command with(group,permrep) allows the use of the abbreviated form of this command.

Examples

Important: The group package has been deprecated. Use the superseding command GroupTheory[PermutationGroup] instead.

 > $\mathrm{with}\left(\mathrm{group}\right):$
 > $g≔\mathrm{grelgroup}\left(\left\{x,y\right\},\left\{\left[x,x,y,x,y,y,y\right],\left[y,y,x,y,x,x,x\right]\right\}\right):$
 > $\mathrm{sg}≔\mathrm{subgrel}\left(\left\{y=\left[y\right]\right\},g\right):$
 > $\mathrm{permrep}\left(\mathrm{sg}\right)$
 ${\mathrm{permgroup}}{}\left({8}{,}\left\{{x}{=}\left[\left[{1}{,}{2}{,}{3}{,}{7}{,}{5}{,}{6}{,}{4}\right]\right]{,}{y}{=}\left[\left[{2}{,}{5}{,}{8}{,}{6}{,}{7}{,}{3}{,}{4}\right]\right]\right\}\right)$ (1)