Unitary groups as stabilizers of orbits (Q2407394)

The author proves the following theorem: Let \(G \leq U ({\mathbb C}^n)\) be a finite unitary group such that some orbit of \(G\) spans \({\mathbb C}^n\) (over \({\mathbb C}\)). Then there is an open and dense subset of elements \(x \in {\mathbb C}^n\) such that \(G = U ( Gx )\). In particular, \(G\) is the setwise stabilizer of one of its orbits