Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical
A gyrogroup is a nonassociative group-like structure modelled on the space of relativistically admissible velocities with a binary operation given by Einstein's velocity addition law. In this article, we present a few of groups sitting inside a gyrogroup G, including the commutator su...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Kashan
2016-01-01
|
| Series: | Mathematics Interdisciplinary Research |
| Subjects: | |
| Online Access: | https://mir.kashanu.ac.ir/article_13907_7d64c578f99c83315fe22b9317d61813.pdf |
| _version_ | 1797630948829822976 |
|---|---|
| author | Teerapong Suksumran |
| author_facet | Teerapong Suksumran |
| author_sort | Teerapong Suksumran |
| collection | DOAJ |
| description | A gyrogroup is a nonassociative group-like structure modelled on the space of relativistically admissible velocities with a binary operation given by Einstein's velocity addition law. In this article, we present a few of groups sitting inside a gyrogroup G, including the commutator subgyrogroup, the left nucleus, and the radical of G. The normal closure of the commutator subgyrogroup, the left nucleus, and the radical of G are in particular normal subgroups of G. We then give a criterion to determine when a subgyrogroup H of a finite gyrogroup G, where the index [G: H] is the smallest prime dividing |G|, is normal in G. |
| first_indexed | 2024-03-11T11:15:03Z |
| format | Article |
| id | doaj.art-0ba546a3bf2748dba0a222159d0a6dd6 |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:15:03Z |
| publishDate | 2016-01-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-0ba546a3bf2748dba0a222159d0a6dd62023-11-11T06:27:31ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652016-01-0111536810.22052/mir.2016.1390713907Special Subgroups of Gyrogroups: Commutators, Nuclei and RadicalTeerapong Suksumran0Department of Mathematics, North Dakota State University, Fargo, ND 58105, USAA gyrogroup is a nonassociative group-like structure modelled on the space of relativistically admissible velocities with a binary operation given by Einstein's velocity addition law. In this article, we present a few of groups sitting inside a gyrogroup G, including the commutator subgyrogroup, the left nucleus, and the radical of G. The normal closure of the commutator subgyrogroup, the left nucleus, and the radical of G are in particular normal subgroups of G. We then give a criterion to determine when a subgyrogroup H of a finite gyrogroup G, where the index [G: H] is the smallest prime dividing |G|, is normal in G.https://mir.kashanu.ac.ir/article_13907_7d64c578f99c83315fe22b9317d61813.pdfgyrogroupcommutator subgyrogroupnucleus of gyrogroupsubgyrogroup of prime indexradical of gyrogroup |
| spellingShingle | Teerapong Suksumran Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical Mathematics Interdisciplinary Research gyrogroup commutator subgyrogroup nucleus of gyrogroup subgyrogroup of prime index radical of gyrogroup |
| title | Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical |
| title_full | Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical |
| title_fullStr | Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical |
| title_full_unstemmed | Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical |
| title_short | Special Subgroups of Gyrogroups: Commutators, Nuclei and Radical |
| title_sort | special subgroups of gyrogroups commutators nuclei and radical |
| topic | gyrogroup commutator subgyrogroup nucleus of gyrogroup subgyrogroup of prime index radical of gyrogroup |
| url | https://mir.kashanu.ac.ir/article_13907_7d64c578f99c83315fe22b9317d61813.pdf |
| work_keys_str_mv | AT teerapongsuksumran specialsubgroupsofgyrogroupscommutatorsnucleiandradical |