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

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16 papers · 1 filter

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.GR2017

Self-similar groups of type FP_{n}

Dessislava H. Kochloukova, Said N. Sidki

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 ap…