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Title: Isolated subgroups of finite abelian groups (English)
Author: Tărnăuceanu, Marius
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 72
Issue: 2
Year: 2022
Pages: 615-620
Summary lang: English
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Category: math
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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. (English)
Keyword: finite abelian group
Keyword: isolated subgroup
Keyword: sum of element orders
MSC: 20K01
MSC: 20K27
idZBL: Zbl 07547223
idMR: MR4412778
DOI: 10.21136/CMJ.2022.0085-21
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Date available: 2022-04-21T19:07:10Z
Last updated: 2024-07-01
Stable URL: http://hdl.handle.net/10338.dmlcz/150420
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Reference: [9] Tărnăuceanu, M.: A generalization of a result on the sum of element orders of a finite group.Math. Slovaca 71 (2021), 627-630. Zbl 07438366, MR 4272885, 10.1515/ms-2021-0008
Reference: [10] Tărnăuceanu, M., Fodor, D. G.: On the sum of element orders of finite Abelian groups.An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 60 (2014), 1-7. Zbl 1299.20059, MR 3252452, 10.2478/aicu-2013-0013
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