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 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 set of elements T of G forming a right transversal for G over H; and
• The corresponding transversal mapping phi: G -> T. If T = [t_1, ..., t_r] and g in G, phi is defined by phi(g) = t_i, where g in H * t_i.