Geodesic
Isolated subgroups of finite abelian groups
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 615-620
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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.
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.
DOI : 10.21136/CMJ.2022.0085-21
Classification : 20K01, 20K27
Keywords: finite abelian group; isolated subgroup; sum of element orders 
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Tărnăuceanu, Marius. Isolated subgroups of finite abelian groups. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 615-620. doi: 10.21136/CMJ.2022.0085-21

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