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 \(\phi: G \rightarrow T\). If \(T = [t_1, \ldots, t_r]\) and \(g \in G\), \(\phi\) is defined by \(\phi(g) = t_i\), where \(g\in H*t_i\).