The interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics

2015/05/22 by Cziszter, K., Domokos, M., Geroldinger, A. · 6 citations
#11B30 #13A15 #13A50 #13F05 #14L24 #20M12 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1505.06059

Abstract

This paper surveys and develops links between polynomial invariants of finite groups, factorization theory of Krull domains, and product-one sequences over finite groups. The goal is to gain a better understanding of the multiplicative ideal theory of invariant rings, and connections between the Noether number and the Davenport constants of finite groups.

Cited by

• Separating versus ordinary Noether numbers
• The Erdős-Ginzburg-Ziv constant of rank-two-like p-groups
• On minimal product-one sequences of maximal length over the non-abelian group of order pq
• On separating sets of polynomial invariants of finite abelian group actions
• A Generalized Davenport Constant of the Second Kind
• Generic orbits, normal bases, and generation degree for fields of rational invariants

Related

• A Generalized Davenport Constant of the Second Kind
• Combinatorial invariants for certain classes of non-abelian groups
• Using Extended Derksen Ideals in Computational Invariant Theory
• Invariant Ideal Axiom
• On syzygies for rings of invariants of abelian groups