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 blackbox groups in which particular words acquire generator status themselves.

AddRedundantGenerators(G, Q) : GrpBB, [ GrpBBElt ] -> GrpBB

A blackbox 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 <= n) and of Q[i] with H.(n + i) is maintained, allowing coercion between G and H and also simple definition of homomorphisms.