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group(deprecated)

 DerivedS
 find the derived series of a given permutation group

 Calling Sequence DerivedS(pg)

Parameters

 pg - group in which the derived series is to be found

Description

 • Important: The group package has been deprecated. Use the superseding command GroupTheory[DerivedSeries] instead.
 • This function finds the derived series of the permutation group pg and it can be used to determine whether pg is solvable or not. The result is returned as a list of unevaluated permgroups call.
 • The command with(group,DerivedS) allows the use of the abbreviated form of this command.

Examples

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

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

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