Abstract
For L a finite non-modular group whose invariants form a polynomial ring and H a subgroup of L containing the derived group of L, Nakajima found necessary and sufficient conditions on H for its invariant ring S H to be a hypersurface. In a crucial step of his proof he showed that if S H is a hypersurface, then between H and L there is a group G with polynomial invariant ring such that S H = S G [ b ] . For G a finite modular p-group over F p with polynomial invariant ring and H a subgroup of G containing the derived group of G, we find necessary and sufficient conditions on H to ensure that S H = S G [ b ] .
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