42.4 Elementary Operations for a Pcgs

returns the list of relative orders of the pcgs pcgs.

the list of relative orders of the pcgs pcgs.

tests whether the relative orders of pcgs are all finite.

tests whether the relative orders of pcgs are prime numbers. Many algorithms require a pcgs to have this property. The operation IsomorphismRefinedPcGroup (see IsomorphismRefinedPcGroup) can be of help here.

returns the subnormal series determined by pcgs.

The group generated by pcgs.

The identity of the group generated by pcgs.

gap> G := Group( (1,2,3,4),(1,2) );; p := Pcgs(G);;
gap> RelativeOrders(p);
[ 2, 3, 2, 2 ]
gap> IsFiniteOrdersPcgs(p);
true
gap> IsPrimeOrdersPcgs(p);
true
gap> PcSeries(p);
[ Group([ (3,4), (2,4,3), (1,4)(2,3), (1,2)(3,4) ]), 
  Group([ (2,4,3), (1,4)(2,3), (1,2)(3,4) ]), 
  Group([ (1,4)(2,3), (1,2)(3,4) ]), Group([ (1,2)(3,4) ]), Group(()) ]

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