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Isolated subgroups of finite abelian groups. (English) Zbl 07547223

Summary: We say that a subgroup \(H\) is isolated in a group \(G\) if for every \(x\in G\) we have either \(x\in H\) or \(\langle x\rangle\cap H=1\). We describe the set of isolated subgroups of a finite abelian group. The technique used is based on an interesting connection between isolated subgroups and the function sum of element orders of a finite group.

MSC:

20K01 Finite abelian groups
20K27 Subgroups of abelian groups
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