Co-word problems and geodesic growth in finitely generated groups (Murray Elder, University of Technology Sydney)

26.05.2020 16:30

For a group with finite symmetric generating set $X$, the co-word problem is the set of words in $X^*$ that are not equal to the identity. We prove that the co-word problem for bounded automata groups is an ET0L language. I will explain what ET0L means (and why you might care). The class of ET0L languages lies between context-free and indexed.

The geodesic growth function counts the number of geodesic words of length $n$. It is bounded below by the usual growth function. An intriguing open question is whether or not a group can have intermediate geodesic growth with respect to some finite symmetric generating set. Candidates are the virtually nilpotent groups and groups with intermediate usual growth. I will discuss work towards this question by myself and my student Alex Bishop.


Join the Zoom session, Att. heure inhabituelle, Séminaire "Groupes et Géométrie"

Organisé par

Section de mathématiques


Murray Elder, University of Technology Sydney

entrée libre


Catégorie: Séminaire

Mots clés: groupes et géométrie

Fichiers joints

geneva-met.pdf118.6 Kb