The separating Noether number of small groups

TL;DR

This paper completes the calculation of the separating Noether numbers for all small groups of order less than 32, providing explicit values and extending previous results.

Contribution

It offers a comprehensive computation of separating Noether numbers for small groups, including general base fields with specific roots of unity.

Findings

Complete list of separating Noether numbers for groups of order less than 32.

Results applicable to general base fields containing specific roots of unity.

Extension of previous partial results to all small groups.

Abstract

The present paper completes the computation of the separating Noether numbers for the groups with order strictly less than $32$. Most of the results are proved for the case of a general (possibly finite) base field containing an element whose multiplicative order equals the size of the group.