Seminario Teoría de Grupos
Self-similar finite p-groups
Ponente: Emerson Melo (University of Brasilia)Fecha: miércoles 27 de noviembre de 2024 - 11:30Lugar: Aula Gris 2, ICMAT
Resumen:
It has been customary to define self-similarity for a group G as the existence of both a subgroup H of G having finite index m in G, and of a homomorphism \(f: H \to G\). Then the group G is self-similar provided the only normal subgroup K of G which is f-invariant subgroup (that is, \(K^f \leq K\)) is trivial. In this case, the triple (G,H,f) is called simple. Such a simple triple leads to a faithful representation of G as a state-closed group of automorphisms of a regular one-rooted tree of degree m. In this talk, we consider a prime p and a finite state-closed p-group G of automorphisms of a regular one-rooted tree of degree p. We present recent results on the structure of G and, in particular, when G admits an injective virtual endomorphism.
