Locally definable subgroups of semialgebraic groups

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 G be an abelian semialgebraic group over a real closed field R and let X be a semialgebraic subset of G. Then the group generated by X contains a generic set and, if connected, it is divisible. More generally, the same result holds when X is definable in any o-minimal expansion of R which is elementarily equivalent to a an,exp. We observe that the above statement is equivalent to saying: there exists an m such that ςi=1m(X - X) is an approximate subgroup of G.