Leírás
The separating Noether number βsep(G) of a finite group G is the minimal positive integer d such that for any finite dimensional complex representation of G, the homogeneous polynomial G-invariants of degree at most d form a separating set. This is modelled on the Noether number β(G). For a finite abelian group G, we have β(G)=D(G), where D(G), the Davenport constant of G is the maximal length of an irreducible zero-sum sequence over G.
An open question in concerning the Davenport constant is whether the equality D((Cn)r)=1+r(n-1) (or β((Cn)r)=1+r(n-1)) holds (where (Cn)r stands for the direct sum of r copies of the cyclic group of order n). As a first part of this talk we will discuss the analogous question on the separating Noether number.
The most common families of finite abelian groups for which the exact value of the Davenport constant is known are the finite abelian groups of rank two and the finite abelian p-groups. Hence it is natural to compute βsep(G) for rank two abelian groups, what will be the second part of the talk.
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