Let G be a finite group and d(G) the minimal number of conjugacy classes that generate G. In any tame realization of G as a Galois group over Q there are at least d(G) ramified primes. The (tame) minimal ramification problem asks whether any group G can be realized (tamely) over Q with exactly d(G) ramified primes. It has been recently proved that this problem has an affirmative answer for a substantial class of finite nilpotent groups (all finite semiabelian nilpotent groups). (Joint work with Hershy Kisilevsky and Jack Sonn)