arXiv subjects

Altair Santos de Oliveira-Tosti

Publications and source records attributed to Altair Santos de Oliveira-Tosti.

3 recordsLinked to original sources

arXiv2026

On the Self-Similarity of Permutational Wreath Products and Their Embedding into Finitely Presented Simple Groups

In this work, we study the self-similarity of permutational wreath products of the form $A \wr_X G$, where $A$ is a finitely generated abelian group and $G$ is a self-similar group (the permutational wreath product $A \wr_X G$ is also known as a lamplighter group). In the case where $G$ is a non-torsion contracting group, we prove that, under certain conditions, the Scott--Röver--Nekrashevych group $V_m(\mathbb{Z}^d \wr_X G)$ is finitely presented and virtually simple. Moreover, we prove that $\mathbb{Z}^d \wr_X G$ embeds into a finitely presented simple group. Furthermore, this provides a new family of groups that satisfy the Boone--Higman conjecture.

math.GR↗

arXiv2023

Thompson-like groups, Reidemeister numbers, and fixed points

We investigate fixed-point properties of automorphisms of groups similar to R. Thompson's group $F$. Revisiting work of Gonçalves-Kochloukova, we deduce a cohomological criterion to detect infinite fixed-point sets in the abelianization, implying the so-called property $R_\infty$. Using the BNS $Σ$-invariant and drawing from works of Gonçalves-Sankaran-Strebel and Zaremsky, we show that our tool applies to many $F$-like groups, including Stein's $F_{2,3}$, Cleary's $F_τ$, the Lodha-Moore groups, and the braided version of $F$.

math.GR↗

arXiv2021

Conjugacy and Centralizers in Groups of Piecewise Projective Homeomorphisms

Monod introduced in [14] a family of Thompson-like groups which provides natural counterexamples to the von Neumann-Day conjecture. We construct a characterization of conjugacy and invariant and use them to compute centralizers in one group of this family.

math.GR↗