Salle séminaire sous-sol (ICJ, bât. Braconnier, UCBL - La Doua)
Salle séminaire sous-sol
ICJ, bât. Braconnier, UCBL - La Doua
Description
A K-approximate subgroup is a subset X of G such that X^2 is contained in at most K
translates of X. The Stabilizer Theorem constructs a subgroup H of the group
generated by X, with H type-definable and of bounded index. This allows not only for
classification resultst in the study of approximate subgroups, but also for explicit
construction of an X^00.
However, this construction uses an expansion L^* of the language L of approximates
subgroups. We will show how to obtain a subgroup H which is L-type definable, using
Udi's theorem together with a result of Schlichting about families of subgroup, in a
model-theoretic version of Ben Yaacov and Wagner, and an old theorem of Beth on
definability.