On a question of Babai and Sós, a model theoretic approach.

par Daniel Palacin (Universität Freiburg )

jeudi 7 mars 2019, 10:30 → 11:30 Europe/Paris

salle 112 Bât Braconnier

In 1985, Babai and Sós asked whether there exists a constant c>0 such that every finite group of order n has a product-free set of size at least cn, where a product-free set of a group is a subset that does not contain three elements x, y and z satisfying xy=z. Gowers showed that the answer is no in the early 2000s, by linking the existence of product-free sets of large density to the existence of low dimensional unitary representations.

In this talk, I will explain how to answer the aforementioned question by model theoretic means.