Subsections

• General Subgroup Constructions

The operators and functions which construct a subgroup of a pc-group always return the subgroup as a pc-group.

H ^ g : GrpPC, GrpPCElt -> GrpPC

Conjugate(H, g) : GrpPC, GrpPCElt -> GrpPC

Construct the conjugate g^(-1) * H * g of the group H under the action of the element g. The group H and the element g must belong to a common group.

H ^ G : GrpPC, GrpPC -> GrpPC

ncl< G | H > : GrpPC, GrpPC -> GrpPC

Given a subgroup H of the group G, construct the normal closure of H in G.

The intersection of groups H and K.

Replace H with the intersection of groups H and K.

CommutatorSubgroup(H, K) : GrpPC, GrpPC -> GrpPC

Construct the commutator subgroup of groups H and K, where H and K are subgroups of a common group G.

Centraliser(G, g) : GrpPC, GrpPCElt -> GrpPC

The centralizer of the element g in the group G.

Centralizer(G, H) : GrpPC, GrpPC -> GrpPC

Centraliser(G, H) : GrpPC, GrpPC -> GrpPC

The centralizer of the group H in the group G.

The maximal normal subgroup of G that is contained in the subgroup H of G.

The normal closure of the subgroup H in the group G.

Normaliser(G, H) : GrpPC, GrpPC -> GrpPC

The normalizer of the subgroup H of the group G.