On the largest $k$-product-free subsets of the Alternating Groups

Seminar series

Junior Number Theory Seminar

Date

Mon, 02 Jun 2025
16:00

Location

Speaker

Anubhab Ghosal

Organisation

University of Oxford

A subset $A$ of $A_n$ is $k$-product-free if for all $a_1,a_2,\dots,a_k\in A$, $a_1a_2\dots a_k$ $\notin A$.
We determine the largest $3$-product-free and $4$-product-free subsets of $A_n$ for sufficiently large $n$. We also obtain strong stability results and results on multiple sets with forbidden cross products. The principal technical ingredient in our approach is the theory of hypercontractivity in $S_n$. Joint work with Peter Keevash.