Abstract: A profinite group can be equipped with its Haar measure to form a probability space, this allows us to talk about random elements in profinite groups. We say that a profinite group is “positively finitely generated” if the probability that k random elements generate a dense subgroup is positive for some k. One can analogously define “positively finitely related” profinite groups. In this talk I will discuss the possibility of defining higher probabilistic finiteness properties for profinite groups. This is joint work with Ged Corob Cook.
Probabilistic finiteness properties for profinite groups