Submission date: 23 July 2024

Abstract:

We answer in the affirmative a conjecture of Berarducci, Peterzil and Pillay [BPP10] for solvable groups, which is an o-minimal version of a particular case of Milnor's isomorphism conjecture [jM83]. We prove that every finite central extension of a definably connected solvable definable group in an o-minimal structure is equivalent to a finite central extension which is definable without additional parameters. The proof relies on an o-minimal adaptation of the higher inflation-restriction exact sequence due to Hochschild and Serre. As in [jM83], we also prove in o-minimal expansions of real closed fields that the conjecture reduces to definably simple groups.

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Full text arXiv 2407.16440: pdf, ps.