| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2022-04-21T19:07:10Z |
| Last updated:
|
2024-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150420 |
| . |
| 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 |
| . |
