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, ..., tr] and g ∈G, φ is defined by φ(g) = ti, where g∈H * ti.
V2.28, 13 July 2023