Definition 1

Let G be a Lie group. An integral subgroup of G is a subgroup H with a connected Lie group structure such that the canonical injection of H into G is an immersion.

A one-parameter subgroup of G is a 1-dimensional integral subgroup of G.

Let H be an integral subgroup of G and i the canonical injection of H into G. Then L(i) defines an isomorphism of L(H) onto a Lie subalgebra of L(G) admitting a topological supplement. L(H) is identified with its image under L(i).