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Power Groups
Power Groups
Parent(G) : GrpPC -> PowerStructure
The PowerStructure of category GrpPC.
PowerGroup(G) : GrpPC -> PowerGroup
The set of all subgroups of G. This is very useful when constructing
sets of pc-groups. If the user will be building a set of subgroups of
a pc-group G, then it is best to specify the set's universe to be
PowerGroup(G). If the set's universe is not specified it will
be Parent(G).
Example GrpPC_PowerGroup (H19E8)
Given the subgroup H of G, construct the set of subgroups
conjugate to H in G using the default set universe.
> G := ExtraSpecialGroup( GrpPC, 2, 2 );
> H := sub< G | Random(G), Random(G) >;
> S := { H^x : x in G };
Given the subgroup H of G, construct the set of subgroups
conjugate to H in G using PowerGroup(G) as the set universe.
> G := ExtraSpecialGroup( GrpPC, 2, 2 );
> H := sub< G | Random(G), Random(G) >;
> P := PowerGroup(G);
> S := { P | H^x : x in G };
The second example will spend far less time in the set constructor and
the resulting set will have faster membership testing.
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