-covering systems of subgroups for classes of -supersoluble and -nilpotent finite groups.
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.
A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.