S. Sidki

activity

20032026

most citedThe Automorphism Tower of Groups acting on Rooted Trees

10 citations · 26 across the 11 of their papers we have counts for

collaborators

19 papers

math.GR2026

On weak commutativity between $n$ isomorphic groups, $n \geq 2$

Said N. Sidki, Noraí R. Rocco, Ricardo N. de Oliveira +1

The Weak Commutativity Group was defined by the first author in the early 1980's as $χ (H) = ⟨ H, H^{ψ} ∣ [h, h^{ψ}] = 1, \forall h \in H ⟩$ where $H$ and $H^{ψ}$ are iso…

math.GR2025

On a Class of Self-Similar Polycyclic Groups

A. C. Dantas, E. de Melo, R. N. de Oliveira +1

A group $G$ is self-similar if it admits a triple $(G, H, f)$ where $H$ is a subgroup of $G$ and $f : H \to G$ a simple homomorphism, that is, the only subgroup $K$ of $H$ , normal in…

math.GR2021

Self-similar abelian groups and their centralizers

Alex C. Dantas, Tulio M. G. Santos, Said N. Sidki

We extend results on transitive self-similar abelian subgroups of the group of automorphisms $A_{m}$ of an $m$ -ary tree $T_{m}$ in \cite{BS}, to the general case wh…

math.GR2020

Intransitive Self-similar Groups

Alex C. Dantas, Tulio M. G. Santos, Said N. Sidki

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 a…

math.GR2018

Self-similar products of groups

Laurent Bartholdi, Said N. Sidki

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 $Z^{(ω)}$ is…

math.RA2018

On Self-Similar Lie Algebras and Virtual Endomorphisms

Vyacheslav Futorny, Dessislava H. Kochloukova, Said N. Sidki

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…