Geodesic
Closure Theorem for Analytic Subgroups of Real Lie Groups
Canadian mathematical bulletin, Tome 19 (1976) no. 4, pp. 435-439

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Let G be a real Lie group, A a closed subgroup of G and B an analytic subgroup of G. Assume that B normalizes A and that AB is closed in G. Then our main result (Theorem 1) asserts that .This result generalizes Lemma 2 in the paper [4], G. Hochschild has pointed out to me that the proof of that lemma given in [4] is not complete but that it can be easily completed. 
Djoković, D. Ž. Closure Theorem for Analytic Subgroups of Real Lie Groups. Canadian mathematical bulletin, Tome 19 (1976) no. 4, pp. 435-439. doi: 10.4153/CMB-1976-065-9
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     author = {Djokovi\'c, D. \v{Z}.},
     title = {Closure {Theorem} for {Analytic} {Subgroups} of {Real} {Lie} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {435--439},
     year = {1976},
     volume = {19},
     number = {4},
     doi = {10.4153/CMB-1976-065-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-065-9/}
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