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

This function finds the Lower Central Series of the permutation group pg and it can be used to find the class of pg and to determine whether pg is nilpotent or not.  The result is returned as a list of unevaluated permgroups call.

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

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

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

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