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The separating Noether number of abelian groups of rank two

Barna Schefler

Abstract

The exact value of the separating Noether number of an arbitrary finite abelian group of rank two is determined. This is done by a detailed study of the monoid of zero-sum sequences over the group.

The separating Noether number of abelian groups of rank two

Abstract

The exact value of the separating Noether number of an arbitrary finite abelian group of rank two is determined. This is done by a detailed study of the monoid of zero-sum sequences over the group.
Paper Structure (5 sections, 15 theorems, 9 equations)

This paper contains 5 sections, 15 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Preparations for the odd order case
  4. A variant of Lemma \ref{['m*geqm']}
  5. Proof of the main theroem

Key Result

Theorem 1.1

Let $\mathop{\ell}\nolimits,n$ be positive integers and denote by $p$ the minimal prime divisor of $n$. Then we have:

Theorems & Definitions (27)

  • Theorem 1.1
  • Remark
  • Definition 2.1
  • Remark
  • Example 2.2
  • Lemma 2.3
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Lemma 2.7
  • ...and 17 more