A rank theorem for analytic maps between power series spaces (Q1805182)

The main result is a rank theorem for analytic mappings (induced by substitution) between spaces of convergent power series. This is used to show that certain isotropy groups are Lie subgroups of infinite- dimensional Lie groups. A spectacular consequence of this result is that reduced hypersurface germs of dimension \(\geq 2\) are determined up to isomorphism by their Lie group of embedded automorphisms.