Finite central extensions of o-minimal groups

2024/07/23 by Baro, Elías, Palacín, Daniel
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2407.16440

Abstract

We answer in the affirmative a conjecture of Berarducci, Peterzil and Pillay \citeBPP10 for solvable groups, which is an o-minimal version of a particular case of Milnor's isomorphism conjecture \citejM83. 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 \citejM83, we also prove in o-minimal expansions of real closed fields that the conjecture reduces to definably simple groups.

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