Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Sidki, Said N."'
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
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
Autor:
Bartholdi, Laurent, Sidki, Said N.
We address the problem of determining the class of self-similar groups, and in particular its closure under restricted direct products. We show that the group $\mathbb Z^{(\omega)}$ is self-similar, that $G^{(\omega)}\rtimes C_2$ is self-similar when
Externí odkaz:
http://arxiv.org/abs/1805.04732
We introduce the notion of virtual endomorphisms of Lie algebras and use it as an approach for constructing self-similarity of Lie algebras. This is done in particular for a class of metabelian Lie algebras having homological type F Pn, which are var
Externí odkaz:
http://arxiv.org/abs/1801.03005
We construct new classes of self-similar groups : S-aritmetic groups, affine groups and metabelian groups. Most of the soluble ones are finitely presented and of type FP_{n} for appropriate n.
Externí odkaz:
http://arxiv.org/abs/1710.04745
Autor:
Dantas, Alex C., Sidki, Said N.
We prove that a self-similar free abelian group has finite rank. We apply the result to self-similar wreath products of abelian groups $G=BwrX$. We show that if $X$ is torsion-free, then $B$ is torsion of finite exponent. Furthemore, we construct a s
Externí odkaz:
http://arxiv.org/abs/1610.08994
Publikováno v:
In Journal of Algebra 1 February 2021 567:564-581
Autor:
Savchuk, Dmytro M., Sidki, Said N.
We introduce a class of automorphisms of rooted $d$-regular trees arising from affine actions on their boundaries viewed as infinite dimensional vector spaces. This class includes, in particular, many examples of self-similar realizations of lampligh
Externí odkaz:
http://arxiv.org/abs/1510.08434
Autor:
Dantas, Alex C., Sidki, Said N.
Let $G_{p,d}$ be the restricted wreath product $C_{p} wr C^{d}$ where $C_{p}$ is a cyclic group of order a prime $p$ and $C^{d}$ a free abelian group of finite rank $d$. We study the existence of faithful state-closed (fsc) representations of $G_{p,d
Externí odkaz:
http://arxiv.org/abs/1505.05165
Publikováno v:
Groups, Geometry, and Dynamics, Volume 7, Issue 2, 323-355, 2013
We study the conjugacy problem in the automorphism group $Aut(T)$ of a regular rooted tree $T$ and in its subgroup $FAut(T)$ of finite-state automorphisms. We show that under the contracting condition and the finiteness of what we call the orbit-sign
Externí odkaz:
http://arxiv.org/abs/1011.2227