Finite central extensions of o-minimal groups
Logic
2025-03-27 v2
Abstract
We answer in the affirmative a conjecture of Berarducci, Peterzil and Pillay \cite{BPP10} for solvable groups, which is an o-minimal version of a particular case of Milnor's isomorphism conjecture \cite{jM83}. We prove that every abstract finite central extension of a definably connected solvable definable group in an o-minimal structure is equivalent to a definable (hence topological) finite central extension. The proof relies on an o-minimal adaptation of the higher inflation-restriction exact sequence due to Hochschild and Serre. As in \cite{jM83}, we also prove in o-minimal expansions of real closed fields that the conjecture reduces to definably simple groups.
Cite
@article{arxiv.2407.16440,
title = {Finite central extensions of o-minimal groups},
author = {Elías Baro and Daniel Palacín},
journal= {arXiv preprint arXiv:2407.16440},
year = {2025}
}