Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.27617 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912986834141184 |
|---|---|
| author | Sercombe, Damian |
| author_facet | Sercombe, Damian |
| contents | We show that any connected algebraic group $G$ over a field admits a nilpotent normal subgroup $Z_\infty(G)$ such that the quotient $G/Z_\infty(G)$ has trivial center. We construct $Z_\infty(G)$ as the final term of the transfinitely extended upper central series of $G$; accordingly, we call it the hypercenter of $G$. We establish several related results about the upper central series of $G$, along with an analogue for algebraic groups of a well-known theorem of Fitting's. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27617 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The hypercenter of an algebraic group Sercombe, Damian Group Theory 20G15 (Primary), 20G07 (Secondary) We show that any connected algebraic group $G$ over a field admits a nilpotent normal subgroup $Z_\infty(G)$ such that the quotient $G/Z_\infty(G)$ has trivial center. We construct $Z_\infty(G)$ as the final term of the transfinitely extended upper central series of $G$; accordingly, we call it the hypercenter of $G$. We establish several related results about the upper central series of $G$, along with an analogue for algebraic groups of a well-known theorem of Fitting's. |
| title | The hypercenter of an algebraic group |
| topic | Group Theory 20G15 (Primary), 20G07 (Secondary) |
| url | https://arxiv.org/abs/2603.27617 |