| Autor: |
Bastos, Raimundo, Dantas, Alex C., de Melo, Emerson |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Archiv der Mathematik (2021). The final publication is available at https://link.springer.com/article/10.1007/s00013-020-01566-w |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00013-020-01566-w |
| Popis: |
Let $G$ be a group. The orbits of the natural action of $\Aut(G)$ on $G$ are called "automorphism orbits" of $G$, and the number of automorphism orbits of $G$ is denoted by $\omega(G)$. Let $G$ be a virtually nilpotent group such that $\omega(G)< \infty$. We prove that $G = K \rtimes H$ where $H$ is a torsion subgroup and $K$ is a torsion-free nilpotent radicable characteristic subgroup of $G$. Moreover, we prove that $G^{'}= D \times \Tor(G^{'})$ where $D$ is a torsion-free nilpotent radicable characteristic subgroup. In particular, if the maximum normal torsion subgroup $\tau(G)$ of $G$ is trivial, then $G^{'}$ is nilpotent. |
| Databáze: |
arXiv |
| Externí odkaz: |
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