| Résume | ABSTRACT: (This is joint work with B. Broer, L. Smith, and P. Webb.) The theorems in the title are classical results in the invariant theory of finite subgroups of $GL_n(C)$ generated by reflections. After reviewing these results, we show how to extend them in several directions, removing many of their hypotheses. In particular, our results work over an arbitrary field $k$ rather than the complex numbers. Also our version of the Chevalley-Shephard-Todd theorem applies to any finite subgroup of $GL_n(k)$, not just reflection groups. If time permits, we will mention the combinatorial applications in characteristic $p$ that motivated us. |
