Rings of invariants of finite groups which are hypersurfaces. II (Q580445)

[For part I see J. Algebra 80, 279-294 (1983; Zbl 0524.14013).] Let V be a finite dimensional complex vector space. An element f of \(GL(V)\) is a ``pseudo-reflection'' if f-id has rank one. Let H be a ``reflection subgroup of \(GL(V)\)'', i.e. a subgroup of GL(V) which is generated by pseudo-reflections. Then the ``order'' of a pseudo- reflection \(f\in H\) is the cardinality of \(\{g\in H| \quad Fix(g)\supseteq Fix(f)\}\) (where \(Fix(f):=\{v\in V| \quad f(v)=v\}.\) Main result: Let G be a finite subgroup of \(SL(V)\). Suppose that \(\dim_{{\mathbb{C}}}(V)>10\) and \(^ GV=\{0\}\). Then the quotient \(V/G\) is a hypersurface iff \(G=\tilde G\cap SL(V)\) for some finite reflection subgroup \(\tilde G\) of \(GL(V)\) in which all orders of pseudo-reflections are equal to the index \([\tilde G:G]\).