In 1951 S. Sato showed that the lattice of subgroups of a modular group with elements of infinite order is isomorphic to the one of a convenient abelian group. Recently in the last part of Sato's work some inexactitudes were found which could question the validity of the result. \par In this paper a new proof of that theorem is provided. Included are also two results on modular groups with elements of infinite order. Namely that any such group can be embedded in a modular group whose torsion- subgroup is divisible and that in case the torsion-subgroup is divisible a modular group splits into the semidirect product of its torsion- subgroup by a cyclic, or locally cyclic, group.

### Projektivitaeten zwischen abelschen und nichtabelschen Gruppen

#### Abstract

In 1951 S. Sato showed that the lattice of subgroups of a modular group with elements of infinite order is isomorphic to the one of a convenient abelian group. Recently in the last part of Sato's work some inexactitudes were found which could question the validity of the result. \par In this paper a new proof of that theorem is provided. Included are also two results on modular groups with elements of infinite order. Namely that any such group can be embedded in a modular group whose torsion- subgroup is divisible and that in case the torsion-subgroup is divisible a modular group splits into the semidirect product of its torsion- subgroup by a cyclic, or locally cyclic, group.
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Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11390/676638`
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