MAGMA Computational Algebra System

Coset Spaces

Subsections

• Coercions Between Groups and Subgroups

Transversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map

RightTransversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map

Given a group G and a subgroup H of G, this function returns:

(a)

An indexed set of elements T of G forming a right transversal for G over H; and,

(b)

The corresponding transversal mapping φ: G -> T. If T = { t₁, ..., t_r } and g in G, φis defined by φ(g) = t_i, where g∈H t_i.

Coercions Between Groups and Subgroups

G ! g : GrpAb, GrpAbElt -> GrpAbElt

Given an element g belonging to the subgroup H of the group G, rewrite g as an element of G.

H ! g : GrpAb, GrpAbElt -> GrpAbElt

Given an element g belonging to the group G, and given a subgroup H of G containing g, rewrite g as an element of H.

K ! g : GrpAb, GrpAbElt -> GrpAbElt

Given an element g belonging to the group H, and a group K, such that H and K are subgroups of G, and both H and K contain g, rewrite g as an element of K.

Morphism(H, G) : GrpAb, GrpAb -> ModMatRngElt

The integer matrix defining the inclusion monomorphism from the subgroup H of G into G.