On the Existence of G-Permutable Subgroups in Alternating Groups Full article
| Journal |
Bulletin of the Malaysian Mathematical Sciences Society
ISSN: 0126-6705 , E-ISSN: 2180-4206 |
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| Output data | Year: 2023, Volume: 46, Number: 5, Article number : 177, Pages count : 16 DOI: 10.1007/s40840-023-01569-0 | ||||
| Tags | Finite group · Alternating group · G-permutable subgroup | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
Recall that a subgroup A of a group G iscalled G-permutable in G if for every subgroup B of G there exists an element x ∈ G such that A and Bx commute. The following question was posed in the Kourovka Notebook: is there an integer n such that for all m > n the alternating group Am has no non-trivial Am-permutable subgroups? We give a positive answer to this question. Moreover, in the case of prime p we prove that Ap has no non-trivial Ap-permutable subgroups except p = 5.
Cite:
Yang N.
, Galt A.
On the Existence of G-Permutable Subgroups in Alternating Groups
Bulletin of the Malaysian Mathematical Sciences Society. 2023. V.46. N5. 177 :1-16. DOI: 10.1007/s40840-023-01569-0 WOS Scopus РИНЦ OpenAlex
On the Existence of G-Permutable Subgroups in Alternating Groups
Bulletin of the Malaysian Mathematical Sciences Society. 2023. V.46. N5. 177 :1-16. DOI: 10.1007/s40840-023-01569-0 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Feb 1, 2023 |
| Accepted: | Jul 28, 2023 |
| Published print: | Aug 21, 2023 |
| Published online: | Aug 21, 2023 |
Identifiers:
| Web of science: | WOS:001052950100002 |
| Scopus: | 2-s2.0-85168468139 |
| Elibrary: | 62802486 |
| OpenAlex: | W4386033335 |
Citing:
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