Generating pairs of projective special linear groups that fail to lift
The following problem was originally posed by B. H. Neumann and H. Neumann. Suppose that a group G can be generated by n elements and that H is a homomorphic image of G. Does there exist, for every generating n‐tuple (h1,…,hn) of H, a homomorphism ϑ:G→H and a generating n‐tuple (g1,…,gn) of G such that (g1ϑ,…,gnϑ)=(h1,…,hn) ?