Polycyclic Products Of Nilpotent Groups

Mathematics Research Report MRR95-003

Polycyclic Products Of Nilpotent Groups

Vittorio D. Almazar and John Cossey

Abstract: In this paper we investigate the structure of polycyclic groups that can be written as the product of two nilpotent groups. We show that if such a group has no finite normal subgroups it is metanilpotent and that its derived length modulo its Fitting subgroup is bounded by the derived lengths of the factors. These results are much more restrictive than the corresponding results for finite groups. We give a construction which we use to show that a polycyclic product of two torsion free nilpotent groups may have any finite group that is the product of two nilpotent groups as torsion subgroup.

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