Soluble Groups with few orbits under automorphisms
| Autor: | Bastos, Raimundo, Dantas, Alex Carrazedo, de Melo, Emerson |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Geometriae Dedicata volume 209, pages119. -- 123 (2020) - The final publication is available at https://link.springer.com/article/10.1007/s10711-020-00525-7 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10711-020-00525-7 |
| 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 $\omega(G)$. We prove that if $G$ is a soluble group with finite rank such that $\omega(G)< \infty$, then $G$ contains a torsion-free characteristic nilpotent subgroup $K$ such that $G = K \rtimes H$, where $H$ is a finite group. Moreover, we classify the mixed order soluble groups of finite rank such that $\omega(G)=3$. Comment: Submitted to an international journal Geometriae Dedicata (2020) |
| Databáze: | arXiv |
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