Addition of Extra Generators

It is often the case that a particular expression in the original generators is important in some homomorphic image of the group in the sense that it will very often form a common subexpression of subsequent expression. For this reason, Magma provides facilities to build related SLP-groups in which particular words acquire generator status themselves.

AddRedundantGenerators(G, Q): GrpSLP, [ GrpSLPElt ] -> GrpSLP

An SLP-group \(H\) on \(n + q\) generators (where \(G\) has \(n\) generators and \(Q\) has \(q\) elements). Furthermore, the identification of \(G.i\) with \(H.i\) (\(i\leq n\)) and of \(Q[i]\) with \(H.(n+i)\) is maintained, allowing coercion between \(G\) and \(H\) and also simple definition of homomorphisms.