Consider a permutation group G defined on d generators. The word group of G is a free group W of rank d. Then we regard G as a homomorphic image of F with associated homomorphism phi: W -> G. All operations involving words in the generators of G will be performed in W.

WordGroup(G) : GrpPerm -> GrpFP, Map

Given a permutation group G defined on d generators, return (a) a free group W on d generators, and (b) the homomorphism phi from W to G such that W.i -> G.i, for i = 1, ..., d. The group W associated with G by this function will be referred to as the word group for G.

Given a permutation group G and its associated word group W with canonical homomorphism phi:W -> G, construct the inverse mapping rho. Thus, given a permutation g of G, g@rho returns an element in the preimage of g under phi. If the word group W does not already exist, it will be created.

Given points x and y belonging to the same G-orbit of the natural G-set X, return a word w in the word group W of G such that x^(phi(w)) = y. Here phi is the canonical homomorphism from W to G.

[Future release] ActingWord(G, Q, R) : GrpPerm, [Elt], [Elt] -> GrpFPElt

Given sequences Q and R, each containing l distinct points lying in the same G-orbit of the natural G-set X of G, return a word in the word group W of G such that Q^(phi(w)) = R. Here phi is the canonical homomorphism from W to G.