Although, in the case of an abelian group, many of the standard
subgroup constructors are trivial, they are all implemented for
the sake of uniformity.
H ^ g : GrpAb, GrpAbElt -> GrpAb
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.
Given a subgroup H of the group G, construct the normal closure of H in G.
Given subgroups H and K of some group G, construct their intersection.
Replace H with the intersection of groups H and K.
Construct the commutator subgroup of groups H and K, where H and K are subgroups of a common group G.
The centralizer of the element g in the group G.
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.
The normalizer of the subgroup H of the group G.
The Sylow p-subgroup for the group G.
The largest normal p-subgroup of the group G.[Next] [Prev] [Right] [Left] [Up] [Index] [Root]