A note on groups with a large permodularly embedded subgroup

It is known that if Gis a group such that the centre factor group G/ζ(G)is polycyclic, then also the commutator subgroup G′is polycyclic. The aim of this paper is to describe this situation from a lattice point of view. It is proved that if Gis a group admitting a permodularly embedded non-periodic subgroup Psuch that the interval [G/P] is a polycyclic lattice, then Gcontains a polycyclic normal subgroup Nsuch that G/Nis quasihamiltonian.