# Seminario Dottorato: “Zeta functions associated to profinite groups”

## Wednesday 1 February 2017, h.14:30 - Room 2BC30 - Leone Cimetta

ARGOMENTI: Seminari Dottorato

Wednesday 1 February 2017 h.14:30, Room 2BC30
In this seminar we will discuss the properties of some Dirichlet series associated to a group $G$ satisfying specific topological properties. These series deal with two important problems arisen in the last century, which both had a great development over the last decades.
The first problem (the subgroup growth of a profinite group $G$) involves the behaviour of the function $a_n(G)$, that is the number of subgroups of $G$ of index $n$.
The second problem consists in determining the probability that, randomly choosing $n$ elements of a group, we get a generating set for the whole group.