The Noether number of the non-abelian group of order 3p
K. Cziszter

TL;DR
This paper establishes degree bounds for polynomial invariants of a specific non-abelian group of order 3p, providing explicit generation and separating system bounds over fields of characteristic zero and coprime to 3p.
Contribution
It proves that the algebra of polynomial invariants is generated by elements of degree at most p+2 for the non-abelian group of order 3p and determines the exact degree bounds for separating systems.
Findings
Invariants generated by elements of degree ≤ p+2
Exact degree bounds for separating systems
Results hold over fields of characteristic zero and not dividing 3p
Abstract
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 degree bound for any separating system of the polynomial invariants of any representation of this group in characteristic not dividing 3p.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · Advanced Algebra and Geometry
