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: | [1] Amiri, H., Amiri, S. M. Jafarian, Isaacs, I. M.: Sums of element orders in finite groups.Commun. Algebra 37 (2009), 2978-2980. Zbl 1183.20022, MR 2554185, 10.1080/00927870802502530 |
Reference: | [2] Busarkin, V. M.: The structure of isolated subgroups in finite groups.Algebra Logika 4 (1965), 33-50 Russian. Zbl 0145.02904, MR 0179249 |
Reference: | [3] Busarkin, V. M.: Groups containing isolated subgroups.Sib. Math. J. 9 (1968), 560-563. Zbl 0192.35301, MR 0237628, 10.1007/BF02199089 |
Reference: | [4] Isaacs, I. M.: Finite Group Theory.Graduate Studies in Mathematics 92. American Mathematical Society, Providence (2008). Zbl 1169.20001, MR 2426855, 10.1090/gsm/092 |
Reference: | [5] : Isolated subgroup.Encyclopedia of Mathematics. Available at https://encyclopediaofmath.org/wiki/Isolated subgroup. |
Reference: | [6] Janko, Z.: Finite $p$-groups with some isolated subgroups.J. Algebra 465 (2016), 41-61. Zbl 1354.20012, MR 3537814, 10.1016/j.jalgebra.2016.06.032 |
Reference: | [7] Kurosh, A. G.: The Theory of Groups. Volume I, II.Chelsea Publishing, New York (1960). Zbl 0064.25104, MR 0109842 |
Reference: | [8] Suzuki, M.: Group Theory. I.Grundlehren der Mathematischen Wissenschaften 247. Springer, Berlin (1982). Zbl 0472.20001, MR 0648772 |
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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