GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II

It is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a pi-group for some finite set pi of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.