group(deprecated)/centralizer - Help

group(deprecated)

 centralizer
 find the centralizer of a set of permutations

 Calling Sequence centralizer(pg, s)

Parameters

 pg - group in which the centralizer is to be found s - set of permutations or a single permutation

Description

 • 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.

Examples

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

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