Coset Tables and Transversals

The functions described in this section apply only to finite groups for which a base and strong generating set may be constructed.

CosetTable(G, H) : Grp, Grp -> Hom(Grp)

The (right) coset table for the group G over subgroup H relative to its defining generators.

Transversal(G, H) : GrpMat, GrpMat -> {@ GrpMatElt @}, Map

RightTransversal(G, H) : GrpMat, GrpMat -> {@ GrpMatElt @}, Map

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

(a)

A 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 ∈G, φ is defined by φ(g) = t_i, where g∈H * t_i.