I wonder if this fact is true:
I consider the exponential map of a Lie group $G$. $$exp: \mathfrak{g} \rightarrow G.$$ Is it true that $exp(0_{T_eG})=e$, where $e$ is the identity element of $G$?
Can someone explain me why? Is it because the one parameter local subgroup associated to $0_{T_eH}$ is constantly equal to $e$ by definition of integral curve? Many thanks.