Article
| 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: | 2022-09-08 |
| 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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