Baro González, ElíasEleftheriou, Pantelis E.Peterzil, Ya’acov2024-10-022024-10-022021-05-19Baro, Elías, Pantelis E. Eleftheriou, y Ya’acov Peterzil. «Locally Definable Subgroups of Semialgebraic Groups». Journal of Mathematical Logic 20, n.o 02 (agosto de 2020): 2050009. https://doi.org/10.1142/S0219061320500099.10.1142/S0219061320500099https://hdl.handle.net/20.500.14352/108512We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. (N.S.) 18(4) (2012) 885–903]. Let GG be an abelian semialgebraic group over a real closed field RR and let XX be a semialgebraic subset of GG. Then the group generated by XX contains a generic set and, if connected, it is divisible. More generally, the same result holds when XX is definable in any o-minimal expansion of RR which is elementarily equivalent to Ran,expℝan,exp. We observe that the above statement is equivalent to saying: there exists an mm such that Σmi=1(X−X)Σi=1m(X−X) is an approximate subgroup of GG.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.1142/S0219061320500099https://www.worldscientific.com/doi/abs/10.1142/S0219061320500099?srsltid=AfmBOoqdVrEQkGeheV789lfxxNcMa2sa5AFqMPH8dM3FAEx6hOpVw938restricted accessÁlgebraLógica simbólica y matemática (Matemáticas)1102.08 Lógica Matemática1201 Álgebra