Explicit Generators of the Invariants of Finite Groups

AbstractLetRdenote a commutative (and associative) ring with 1 and letAdenote a finitely generated commutativeR-algebra. LetGdenote a finite group ofR-algebra automorphisms ofA. In the case thatRis a field of characteristic 0, Noether constructed a finite set ofR-algebra generators of the invariants ofG. This paper proves that the same construction produces a set of generators of the invariants ofGwhen |G|! is invertible inR. Generators of the invariants ofGare also explicitly described in the case thatGis solvable and |G| is invertible inR