Regular rings of invariants of unipotent groups
Let V be an n-dimensional vector space over a prime field K of characteristic \(p>0\) and G a finite subgroup of GL(V). Then G acts naturally on the symmetric algebra K[V] of V. Let \(K[V]^ G\) be the subring of K[V] consisting of all invariant polynomials which are algebraically independent over K. The main result of the paper is the following Theorem. Suppose that G is the direct product of a p-subgroup N and a p'-subgroup H (i.e. \((| H|,p)=1)\) of G. Then the following conditions are equivalent: (1) \(K[V]^ G\) is a polynomial ring over K. (2) H is generated by pseudo-reflections in GL(V) and there is a K-basis \(\{X_ i| \quad 1\leq i\leq n\}\) of V such that \(\prod^{n}_{i=1}| NX_ i| =| N|\) and all \(\oplus^{j}_{i=1}KX_ i\quad(1\leq j\leq n)\) are KN-submodules of V.
scientific article; zbMATH DE number 3851374