The n-ary adding machine and solvable groups
| Autor: | Josimar Da Silva Rocha, Said Sidki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | International Journal of Group Theory, Vol 2, Iss 4, Pp 43-88 (2013) |
| Druh dokumentu: | article |
| ISSN: | 2251-7650 2251-7669 |
| Popis: | We describe under a various conditions abelian subgroups of the automorphism group $Aut(T_n)$ of the regular $n$-ary tree $T_n$, which are normalized by the $n$-ary adding machine $tau=(e,dots, e,tau)sigma_tau$ where $sigma_tau$ is the $n$-cycle $(0, 1,dots, n-1)$. As an application, for $n=p$ a prime number, and for $n=p^2$ when $p=2$, we prove that every finitely generated soluble subgroup of $Aut(T_n)$, containing $tau$ is an extension of a torsion-free metabelian group by a finite group. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|