The spectrum of group-based complete Latin squares (Q2315436)

Summary: We construct sequencings for many groups that are a semi-direct product of an odd-order abelian group and a cyclic group of odd prime order. It follows from these constructions that there is a group-based complete Latin square of order \(n\) if and only if \(n \in \{ 1,2,4\}\) or there is a non-abelian group of order \(n\).