group(deprecated)/normalizer - Maple Help

group(deprecated)

 normalizer
 Find the normalizer of a subgroup

 Calling Sequence normalizer(pg, sg)

Parameters

 pg, sg - two permgroups of the same degree

Description

 • Important: The group package has been deprecated. Use the superseding command GroupTheory[Normalizer] instead.
 • This function finds the largest subgroup of pg in which sg is a normal subgroup. The group sg should be a subgroup of pg.  The result is returned as an unevaluated permgroup call.
 • The command with(group,normalizer) allows the use of the abbreviated form of this command.

Examples

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

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