group(deprecated)/Sylow - Maple Help

group(deprecated)

 Sylow
 find the Sylow-p-subgroup of a permutation group

 Calling Sequence Sylow(pg, p)

Parameters

 pg - group in which the Sylow-p-subgroup is to be found p - prime divisor of the order of pg

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{group}\right):$
 > $G≔\mathrm{permgroup}\left(5,\left\{\left[\left[1,2\right]\right],\left[\left[1,2,3,4,5\right]\right]\right\}\right):$
 > $\mathrm{ifactor}\left(\mathrm{grouporder}\left(G\right)\right)$
 ${\left({2}\right)}^{{3}}{}\left({3}\right){}\left({5}\right)$ (1)
 > $S≔\mathrm{Sylow}\left(G,2\right)$
 ${S}{≔}{\mathrm{permgroup}}{}\left({5}{,}\left\{\left[\left[{2}{,}{5}\right]\right]{,}\left[\left[{1}{,}{5}{,}{4}{,}{2}\right]\right]\right\}\right)$ (2)
 > $\mathrm{grouporder}\left(S\right)$
 ${8}$ (3)