Common divisor graphs for skew braces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910809006800896 |
|---|---|
| author | Properzi, Silvia Van Antwerpen, Arne |
| author_facet | Properzi, Silvia Van Antwerpen, Arne |
| contents | We introduce two common divisor graphs associated with a finite skew brace, based on its $λ$- and $θ$-orbits. We prove that the number of connected components is at most two and the diameter of a connected component is at most four. Furthermore, we investigate their relationship with isoclinism. Similarly to its group theoretic inspiration, the skew braces with a graph with two disconnected vertices are very restricted and are determined. Finally, we classify all finite skew braces with a graph with one vertex, where four infinite families arise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12415 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Common divisor graphs for skew braces Properzi, Silvia Van Antwerpen, Arne Combinatorics Group Theory 16T25, 05C25, 20N99 We introduce two common divisor graphs associated with a finite skew brace, based on its $λ$- and $θ$-orbits. We prove that the number of connected components is at most two and the diameter of a connected component is at most four. Furthermore, we investigate their relationship with isoclinism. Similarly to its group theoretic inspiration, the skew braces with a graph with two disconnected vertices are very restricted and are determined. Finally, we classify all finite skew braces with a graph with one vertex, where four infinite families arise. |
| title | Common divisor graphs for skew braces |
| topic | Combinatorics Group Theory 16T25, 05C25, 20N99 |
| url | https://arxiv.org/abs/2306.12415 |