New examples of infinite n-periodic groups (Dominik Gruber, ETHZ)

02.04.2019 10:30

Burnside's problem on the existence of infinite finitely generated n-periodic groups was one of the major questions of 20th century combinatorial group theory. While we by now know that such groups exist, producing examples satisfying additional interesting properties has remained a notoriously difficult task.

We will discuss two results providing such examples. The first result (joint work with Remi Coulon) is based on small cancellation theory and yields an explicit and easy-to-apply, yet powerful method for constructing infinite finitely generated n-periodic groups. The second result (joint work with John Mackay) shows that, in a suitable model for random groups, generic quotients of free Burnside groups are infinite.
Both proofs rely on constructing acylindrical actions of groups on Gromov hyperbolic spaces.

Lieu

Room 623, Séminaire "Groupes et Géométrie"

entrée libre