Finite central extensions of o-minimal groups

Elías Baro; Daniel Palacín

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arXiv · 2407.16440

Finite central extensions of o-minimal groups

Elías Baro·Daniel Palacín

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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.

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BibTeX RIS

Elías Baro, Daniel Palacín. 2024-07-23. Finite central extensions of o-minimal groups. https://arxiv.org/abs/2407.16440

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