RT Journal Article
T1 Locally definable subgroups of semialgebraic groups
A1 Baro González, Elías
A1 Eleftheriou, Pantelis E.
A1 Peterzil, Ya’acov
AB We 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.
PB World Scientific Europe
YR 2021
FD 2021-05-19
LK https://hdl.handle.net/20.500.14352/108512
UL https://hdl.handle.net/20.500.14352/108512
LA eng
NO Baro, 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.
NO MTM2014-59178-P, MTM2017-82105-P and Grupos UCM 910444.
DS Docta Complutense
RD 9 abr 2025