Bounds on the order of generation of SO(n,R) by one-parameter subgroups (Q804720)

Let G be a compact Lie group and \(X_ 1,...,X_ k\) a set of generators of its Lie algebra \({\mathfrak g}\). Then any element of G can be written as a finite product of exponentials exp \(t_ jX_ j\), \(j\in \{1,...,k\}\). The author addresses the question how many factors of this kind one needs. For \(G=SO(n)\) he constructs various sets of generators via a successive use of the Cartan decomposition of G when viewed as the group of isometries of a compact Riemannian symmetric space. Then he gives uniform bounds for the number of factors needed. In the case SO(3) he shows that any two elements of \({\mathfrak g}\) which are not collinear can be used as generators and calculates the minimal number of factors in terms of the angle between the two infinitesimal rotations (i.e. their axes).