Let F be a C∞-foliation on a compact C∞-manifold M. We consider the group of all leaf preserving C∞-diffeomorphisms of (M, F) which are isotopic to the identity through leaf preserving C∞-diffeomorphisms. Then we show that the group is simple if and only if all leaves of F are dense.
Kazuhiko FUKUI. "The necessary and sufficient condition for the group of leaf preserving diffeomorphisms to be simple." J. Math. Soc. Japan 64 (1) 181 - 184, January, 2012. https://doi.org/10.2969/jmsj/06410181