等質左リー・ループの正規左リー部分ループについて

We show that any homogeneous left loop is characterized by the homogeneous system associated with it. By applying this result to the theory of normal subsystems of analytic homogeneous systems developed in [5], we show the fundamental theorems concerning normal left Lie subloops of homogeneous left Lie loops, an exact generalization of the theory of Lie groups and Lie algebras.