2018
Jun
11

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

10:00am to 10:50am

## Location:

Feldman Building, Givat Ram

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.

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.