The separating Noether number of 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.

The parts of the previous version on the groups with a cyclic subgroup of index two and on the groups of order at most sixteen are moved to a separate article entitled "Separating versus ordinary Noether numbers"