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

If sub is a subgrel, then elem should be a word in the group generators. A two-element list will be returned. The first element is the subgroup element expressed as a word in the subgroup generators, the second is the right coset representative. The coset representative will be an element of the set returned by cosets(sub).

If sub is a permgroup, then elem should be a permutation in disjoint cycle notation. A two-element list is returned. The first element is a permutation contained in sub, the second is a right coset representative permutation for sub in the symmetric group of the same degree. The coset representative will be an element of the set returned by cosets(Sn, sub), where Sn is the symmetric group of the same degree as sub.

The command with(group,cosrep) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{group}\right)\:$

$g≔\mathrm{grelgroup}\left(\left\{a\,b\,c\right\}\,\left\{\left[a\,b\,c\,a\,\frac{1}{b}\right]\,\left[b\,c\,a\,b\,\frac{1}{c}\right]\,\left[c\,a\,b\,c\,\frac{1}{a}\right]\right\}\right)\:$

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

$\left[\left[y\,y\,y\,y\,y\right]\,\left[a\right]\right]$

$\mathrm{pg}≔\mathrm{permgroup}\left(7\,\left\{\left[\left[1\,2\,3\right]\right]\,\left[\left[3\,4\,5\,6\,7\right]\right]\right\}\right)\:$

$\mathrm{cosrep}\left(\left[\left[3\,4\,5\,6\right]\right]\,\mathrm{pg}\right)$

$\left[\left[\left[3\,4\,5\,7\,6\right]\right]\,\left[\left[6\,7\right]\right]\right]$