# Algebra Seminar talk

2024-05-24 16:00! Sem.R. DB gelb 10!

Zaniar **Ghadernezhad***The small index property of some Hrushovski constructions*

Abstract:

A topological group G has the small index property if every small index subgroup of G is open. The topological groups that we consider are automorphism groups of saturated countable structures with the pointwise convergence topology. The small index property of an automorphism group, when the structure is $\omega$-categorical, leads to so-called `reconstruction' of the structure up to bi-interpretability merely based on the automorphism group. In the talk, I will review general techniques for proving the small index property of automorphism groups and key properties of Hrushovski constructions. Then, I will demonstrate the small index property of the automorphism groups of some Hrushovski constructions. This is a revisit of an older result with some new insights and observations.