The proportion of derangements characterizes the symmetric and alternating groups
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910465957822464 |
|---|---|
| author | Poonen, Bjorn Slavov, Kaloyan |
| author_facet | Poonen, Bjorn Slavov, Kaloyan |
| contents | Let $G$ be a subgroup of the symmetric group $S_n$. If the proportion of fixed-point-free elements in $G$ (or a coset) equals the proportion of fixed-point-free elements in $S_n$, then $G=S_n$. The analogue for $A_n$ holds if $n \ge 7$. We give an application to monodromy groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_02724 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The proportion of derangements characterizes the symmetric and alternating groups Poonen, Bjorn Slavov, Kaloyan Group Theory Algebraic Geometry Primary 20B35, Secondary 11A63, 14E20, 14G15, 20B10 Let $G$ be a subgroup of the symmetric group $S_n$. If the proportion of fixed-point-free elements in $G$ (or a coset) equals the proportion of fixed-point-free elements in $S_n$, then $G=S_n$. The analogue for $A_n$ holds if $n \ge 7$. We give an application to monodromy groups. |
| title | The proportion of derangements characterizes the symmetric and alternating groups |
| topic | Group Theory Algebraic Geometry Primary 20B35, Secondary 11A63, 14E20, 14G15, 20B10 |
| url | https://arxiv.org/abs/2107.02724 |