A subgroup H of an Abelian group G is called fully inert if (φH + H)/H is finite for every φ ∈ End(G). Fully inert subgroups of free Abelian groups are characterized. It is proved that H is fully inert in the free group G if and only if it is commensurable with nG for some n ≥ 0, that is, (H + nG)/H and (H + nG)/nG are both finite. From this fact we derive a more structural characterization of fully inert subgroups H of free groups G, in terms of the Ulm–Kaplansky invariants of G/H and the Hill–Megibben invariants of the exact sequence 0 → H → G → G/H → 0.

Fully inert subgroups of free Abelian groups

SALCE, LUIGI;ZANARDO, PAOLO
2014

Abstract

A subgroup H of an Abelian group G is called fully inert if (φH + H)/H is finite for every φ ∈ End(G). Fully inert subgroups of free Abelian groups are characterized. It is proved that H is fully inert in the free group G if and only if it is commensurable with nG for some n ≥ 0, that is, (H + nG)/H and (H + nG)/nG are both finite. From this fact we derive a more structural characterization of fully inert subgroups H of free groups G, in terms of the Ulm–Kaplansky invariants of G/H and the Hill–Megibben invariants of the exact sequence 0 → H → G → G/H → 0.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3047899
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