We consider the group of Lipschitz homeomorphisms of a Lipschitz manifold and its subgroups. First we study properties of Lipschitz homeomorphisms and show the local contractibility and the perfectness of the group of Lipschitz homeomorphisms. Next using this result we can prove that the identity component of the group of equivariant Lipschitz homeomorphisms of a principal -bundle over a closed Lipschitz manifold is perfect when is a compact Lie group.
Kōjun ABE. Kazuhiko FUKUI. "On the structure of the group of Lipschitz homeomorphisms and its subgroups." J. Math. Soc. Japan 53 (3) 501 - 511, July, 2001. https://doi.org/10.2969/jmsj/05330501