Geodesic
Uniform Finite Generation of Threedimensional Linear Lie Groups
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 396-417

Voir la notice de l'article provenant de la source Cambridge University Press

A connected Lie group G is generated by one-parameter subgroups exp(tX1), ... , exp(tXk) if every element of G can be written as a finite product of elements chosen from these subgroups. This happens just in case the Lie algebra of G is generated by the corresponding infinitesimal transformations X1, ... , Xk ; indeed the set of all such finite products is an arcwise connected subgroup of G, and hence a Lie subgroup by Yamabe's theorem [9]. If there is a positive integer n such that every element of G possesses such a representation of length at most n, G is said to be uniformly finitely generated by the one-parameter subgroups. 
Koch, R. M.; Lowenthal, Franklin. Uniform Finite Generation of Threedimensional Linear Lie Groups. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 396-417. doi: 10.4153/CJM-1975-048-0
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