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 $n$.
@article{10_37236_8542,
author = {M. A. Ollis and Christopher R. Tripp},
title = {The spectrum of group-based complete {Latin} squares},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8542},
zbl = {1417.05020},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8542/}
}
TY - JOUR
AU - M. A. Ollis
AU - Christopher R. Tripp
TI - The spectrum of group-based complete Latin squares
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8542/
DO - 10.37236/8542
ID - 10_37236_8542
ER -
%0 Journal Article
%A M. A. Ollis
%A Christopher R. Tripp
%T The spectrum of group-based complete Latin squares
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8542/
%R 10.37236/8542
%F 10_37236_8542
M. A. Ollis; Christopher R. Tripp. The spectrum of group-based complete Latin squares. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8542
