Resumen de Invariant Theory of Abelian Transvection Groups

• Let G be a finite group acting linearly on the vector space V over a field of arbitrary characteristic. The action is called \emph{coregular} if the invariant ring is generated by algebraically independent homogeneous invariants, and the \emph{direct summand property} holds if there is a surjective k[V]G-linear map :k[V]k[V]G. The following Chevalley--Shephard--Todd type theorem is proved. Suppose G is abelian. Then the action is coregular if and only if G is generated by pseudo-reflections and the direct summand property holds.