Workshop on Additive Combinatorics and Algebraic Connections
Product Free Sets in Groups
Abstract: A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product free subset of the alternating group $A_n$ be?
In the talk we will completely solve the problem by determining the largest product free subset of $A_n$. Our proof combines a representation theoretic argument due to Gowers, with a new analytic tool called hypercontractivity for global functions.
Based on a joint work with Peter Keevash and Dor Minzer