Seminario Teoría de Grupos ICMAT-UAM

Jueves 21/2/2019, 11:30, Aula 520, UAM

Speaker: MariaLaura Noce (Università degli Studi di Salerno)

Tittle: Engel conditions in some groups of automorphisms of rooted trees

Abstract: Groups of automorphisms of $d$-adic rooted trees ($AutT_d$ for short) have been studied for years as an important source of groups with interesting properties. For example, many of their subgroups constitute a counterexample to the General Burnside Problem. The question whether every Engel group is locally nilpotent is the analogue of the general Burnside problem in the realm of Engel groups. Recall that an element $x$ of a group $G$ is said to be left Engel  if for any $g in G$ there exists an integer $n = n(g, x) geq 1$ such that $[g,_n x] = 1$. We denote this set by $L(G)$. If $L(G) = G$,  we say that $G$ is an Engel group.

In this talk, we introduce basic notions of the theory of groups of automorphisms acting on $d$-adic rooted trees and some of its subgroups like fractal and (weakly) branch groups. Then we will present known results and open problems about Engel conditions in different families of subgroups of $AutT_d$

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