Seminario Teoría de grupos 17/03


11:30 Aula Naranja ICMAT

Speaker: Jordi Delgado (Universitat Politècnica de Catalunya)

Title: Relative order and spectrum: three questions and two answers

Abstract: We consider a natural generalization of the concept of order of an element in a group: an element g ∈ G is said to have (relative) order k in a subgroup H of G if k is the first strictly positive integer such that g^k ∈ H. We use Stallings-like automata to study this notion and its algorithmic properties in the realm of free groups and some related families. In this talk, I will briefly survey the main concepts introduced in this work, discuss some natural questions on them, and present both positive and negative (algorithmic) results we have obtained. This is joint work with Enric Ventura and Alexander Zakharov.