General symbols and presentations of elementary linear groups.
We give an algebraic proof of the fact that a generating set of the mapping class group Mg,1 (g ≥ 3) may be obtained by replicating a generating set of M2,1.
We study the generation of finite groups by nilpotent subgroups and in particular we investigate the structure of groups which cannot be generated by nilpotent subgroups and such that every proper quotient can be generated by nilpotent subgroups. We obtain some results about the structure of these groups and a lower bound for their orders.