Profinite groups of finite probabilistic virtual rank
Matteo Vannacci (University of the Basque Country)
Abstract: A profinite group $G$ carries naturally the structure of a probability space, namely with respect to its normalised Haar measure. We study the probability $Q(G,k)$ that $k$ Haar-random elements generate an open subgroup in the profinite group $G$. In particular, in this talk I will introduce the probabilistic virtual rank $\mathrm{pvr}(G)$ of $G$; that is, the smallest $k$ such that $Q(G,k)=1$. We will discuss some key theorems and open problems about random generation in profinite groups, with a view toward finite direct products of hereditarily just infinite profinite groups. Classic examples of the latter type of groups are semisimple algebraic groups over non-archimedean local fields. This is joint work with Benjamin Klopsch and Davide Veronelli.
group theory
Audience: researchers in the topic
| Organizers: | Angela Carnevale, Joshua Maglione*, Tobias Rossmann |
| *contact for this listing |