Zero-separating invariants for finite groups

Separating Invariants and Finite Reflection Groups

Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a more geometric notion of separating algebra. This allows us to prove that when there is a polynomial separating algebra, the group is generated by reflections, and when there is a complete int...

Explicit separating invariants for cyclic P-groups

We consider a finite dimensional indecomposable modular representation of a cyclic p-group and we give a recursive description of an associated separating set: We show that a separating set for a representation can be obtained by adding to a separating set for any subrepresentation some explicitly defined invariant polynomials. Meanwhile, an explicit generating set for the invariant ring is kno...

Two zero-sum invariants on finite abelian groups

Let G be an additive finite abelian group with exponent exp(G). Let s(G) (resp. η(G)) be the smallest integer t such that every sequence of t elements (repetition allowed) from G contains a zero-sum subsequence T of length |T | = exp(G) (resp. |T | ∈ [1, exp(G)]). Let H be an arbitrary finite abelian group with exp(H) = m. In this paper, we show that s(Cmn ⊕ H) = η(Cmn ⊕ H) + mn − 1 holds for a...

Separating Invariants for Modular P -groups and Groups Acting Diagonally

We study separating algebras for rings of invariants of finite groups. We describe a separating subalgebra for invariants of p-groups in characteristic p using only transfers and norms. Also we give an explicit construction of a separating set for invariants of groups acting diagonally. Let F be an algebraically closed field and let G be a finite group. Consider a faithful representation ρ : G ...

Constructing Invariants for Finite Groups