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

This function finds a maximal p-group sitting inside the permutation group pg. The given permutation group pg must have small order and degree. The result is returned as an unevaluated permgroup call.

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

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

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

$\mathrm{ifactor}\left(\mathrm{grouporder}\left(G\right)\right)$

${\left(2\right)}^3\left(3\right)\left(5\right)$

$S≔\mathrm{Sylow}\left(G\,2\right)$

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

$\mathrm{grouporder}\left(S\right)$

$8$