Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Dantas, Alex A."'
In this paper we prove that a free nilpotent group of finite rank is transitive self-similar. In contrast, we prove that a free metabelian group of rank $r \geq 2$ is not transitive self-similar.
Externí odkaz:
http://arxiv.org/abs/2406.10665
A finitely generated group is said to be an automata group if it admits a faithful self-similar finite-state representation on some regular $m$-tree. We prove that if $G$ is a subgroup of an automata group, then for each finitely generated abelian gr
Externí odkaz:
http://arxiv.org/abs/2405.16678
We extend results on transitive self-similar abelian subgroups of the group of automorphisms $\mathcal{A}_m$ of an $m$-ary tree $\mathcal{T}_m$ in \cite{BS}, to the general case where the permutation group induced on the first level of the tree has $
Externí odkaz:
http://arxiv.org/abs/2110.02441
Publikováno v:
Archiv der Mathematik (2021). The final publication is available at https://link.springer.com/article/10.1007/s00013-020-01566-w
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)< \in
Externí odkaz:
http://arxiv.org/abs/2008.10800
A group is said to be self-similar provided it admits a faithful state-closed representation on some regular $m$-tree and the group is said to be transitive self-similar provided additionally it induces transitive action on the first level of the tre
Externí odkaz:
http://arxiv.org/abs/2004.08941
Publikováno v:
Geometriae Dedicata volume 209, pages119. -- 123 (2020) - The final publication is available at https://link.springer.com/article/10.1007/s10711-020-00525-7
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 t
Externí odkaz:
http://arxiv.org/abs/1908.01375
Let $p$ be a prime and $G$ a pro-$p$ group of finite rank that admits a faithful, self-similar action on the $p$-ary rooted tree. We prove that if the set $\{g\in G \ | \ g^{p^n}=1\}$ is a nontrivial subgroup for some $n$, then $G$ is a finite $p$-gr
Externí odkaz:
http://arxiv.org/abs/1905.12482
Autor:
Bastos, Raimundo A., Dantas, Alex C.
Publikováno v:
Journal of Algebra Volume 516, 15 December 2018, Pages 401-413
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 $\omega(G)$. In this paper we prove that if $G$ is an FC-group with finitely m
Externí odkaz:
http://arxiv.org/abs/1806.11132
Let $G$ be a finite group with the property that if $a,b$ are powers of $\delta_1^*$-commutators such that $(|a|,|b|)=1$, then $|ab|=|a||b|$. We show that $\gamma_{\infty}(G)$ is nilpotent.
Externí odkaz:
http://arxiv.org/abs/1710.10712
Publikováno v:
Groups, Geometry & Dynamics; 2024, Vol. 18 Issue 4, p1369-1375, 7p
