Baro González, ElíasPalacín Cruz, Daniel2025-10-072025-10-0720250025-58741432-182310.1007/s00209-025-03796-6https://hdl.handle.net/20.500.14352/1246292025 Acuerdos transformativos CRUEWe answer in the affirmative a conjecture of Berarducci et al. (Confl. Math. 2(4): 473–496, 2010) for solvable groups, which is an o-minimal version of a particular case of Milnor’s isomorphism conjecture (Milnor, Comment Math Helv 58(1): 72–85, 1983). 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 Milnor (Comment Math Helv 58(1): 72–85, 1983), we also prove in o-minimal expansions of real closed fields that the conjecture reduces to definably simple groups.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal articlehttps://doi.org/10.1007/s00209-025-03796-6open accesso-MinimalCentral extensionSecond cohomologyLógica simbólica y matemática (Matemáticas)Grupos (Matemáticas)1102.10 Teoría de Modelos1210.08 Grupos de Lie