One-parameter subgroup

Summary

A one-parameter subgroup of a topological group $G$ is a continuous group homomorphism from the additive group $\R$ into $G$. In a Lie group, it is a smooth curve through the identity along which the group law becomes addition of the parameter. One-parameter subgroups of a Lie group correspond to the tangent vectors at the identity, which is how the exponential map is built.