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

This function finds the largest subgroup of the permutation group pg in which every element commutes with every element of s. s need not be contained in pg.  The result is returned as an unevaluated permgroup call.

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

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

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

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

$\mathrm{centralizer}\left(\mathrm{permgroup}\left(5\,\left\{\left[\left[1\,2\,3\right]\right]\,\left[\left[3\,4\,5\right]\right]\right\}\right)\,\left[\left[1\,2\right]\right]\right)$

$\mathrm{permgroup}\left(5\,\left\{\left[\left[3\,4\,5\right]\right]\,\left[\left[1\,2\right]\,\left[4\,5\right]\right]\right\}\right)$