The Noether number of the non-abelian group of order \(3p\). (English) Zbl 1349.13013
Summary: It is proven that for any representation over a field of characteristic \(0\) of the non-abelian semidirect product of a cyclic group of prime order \(p\) and the group of order \(3\) the corresponding algebra of polynomial invariants is generated by elements of degree at most \(p + 2\). We also determine the exact universal degree bound for separating systems of polynomial invariants of this group in characteristic not dividing \(3p\).
MSC:
| 13A50 | Actions of groups on commutative rings; invariant theory |
| 11B75 | Other combinatorial number theory |
| 13A02 | Graded rings |
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