Geodesic
Uniform Finite Generation of the Isometry Groups of Euclidean and Non-Euclidean Geometry
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 364-373

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A connected Lie group H is generated by a pair of oneparameter subgroups if every element of H can be written as a finite product of elements chosen alternately from the two one-parameter subgroups. If, moreover, there exists a positive integer n such that every element of H possesses such a representation of length at most n, then H is said to be uniformly finitely generated by the pair of one-parameter subgroups. In this case, define the order of generation of H as the least such n; otherwise define it as infinity.For the isometry group of the spherical geometry, or equivalently for the rotation group SO(3), the order of generation is always finite. 
Lowenthal, Franklin. Uniform Finite Generation of the Isometry Groups of Euclidean and Non-Euclidean Geometry. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 364-373. doi: 10.4153/CJM-1971-037-5
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