Non-split sharply 2-transitive groups of bounded exponent
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909791140446208 |
|---|---|
| author | Amelio, Marco |
| author_facet | Amelio, Marco |
| contents | We construct here the first known examples of non-split sharply 2-transitive groups of bounded exponent in odd positive characteristic for every large enough prime $p \equiv 3 \pmod{4}$. In fact, we show that there are countably many pairwise non-isomorphic countable non-split sharply 2-transitive groups of characteristic $p$ for each such $p$. Furthermore, we construct non-periodic non-split sharply 2-transitive groups (of these same characteristics) with centralizers of involutions of bounded exponent. As a consequence of these results, we answer two open questions about sharply 2-transitive and 2-transitive permutation groups. The constructions of groups as announced rely on iteratively applying (geometric) small cancellation methods in the presence of involutions. To that end, we develop a method to control some small cancellation parameters in the presence of even-order torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-split sharply 2-transitive groups of bounded exponent Amelio, Marco Group Theory We construct here the first known examples of non-split sharply 2-transitive groups of bounded exponent in odd positive characteristic for every large enough prime $p \equiv 3 \pmod{4}$. In fact, we show that there are countably many pairwise non-isomorphic countable non-split sharply 2-transitive groups of characteristic $p$ for each such $p$. Furthermore, we construct non-periodic non-split sharply 2-transitive groups (of these same characteristics) with centralizers of involutions of bounded exponent. As a consequence of these results, we answer two open questions about sharply 2-transitive and 2-transitive permutation groups. The constructions of groups as announced rely on iteratively applying (geometric) small cancellation methods in the presence of involutions. To that end, we develop a method to control some small cancellation parameters in the presence of even-order torsion. |
| title | Non-split sharply 2-transitive groups of bounded exponent |
| topic | Group Theory |
| url | https://arxiv.org/abs/2509.11958 |