On the n-transitivity of the group of equivariant diffeomorphisms

Abstract Let G be a Lie group and let M be a proper smooth G -manifold. If M is connected and $$\dim (M)\ge 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>dim</mml:mo> <mml:mo>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo>)</mml:mo> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , the group of diffeomorphisms of M , that are isotopic to the identity through a compactly supported isotopy, acts n -transitively on M , for any n . In this paper, we prove a version of the n -transitivity result for the group of equivariant diffeomorphisms of M . As a corollary we obtain a result concerning diffeomorphisms of the orbit space M / G . A special case of the result for orbit spaces gives an n -transitivity result for orbifold diffeomorphisms that was earlier proved by F. Pasquotto and T. O. Rot.