HD-Combinatorics: Aner Shalev, "Probabilistically nilpotent groups"

In the past decades There has been considerable interest in the probability that two random elements of (finite or certain infinite)
groups commute.
I will describe new works (by myself and by others) on probabilistically nilpotent groups, namely groups in which the probability that [x_1,...,x_k]=1 is positive/bounded away from zero.
It turns out that, under some natural conditions,
these are exactly the groups which have a finite/bounded index
subgroup which is nilpotent of class < k.
The proofs have some combinatorial flavor.


Mon, 11/06/2018 - 10:00 to 10:50


Feldman Building, Givat Ram