Constructing R-sequencings and terraces for groups of even order

The problem of finding R-sequencings for abelian groups of even orders has been reduced to that of finding R$^*$-sequencings for abelian groups of odd orders except in the case when the Sylow 2-subgroup is a non-cyclic non-elementary-abelian group of order 8. We partially address this exception, including all instances when the group has order $8t$ for $t$ congruent to 1, 2, 3 or 4 $(\operatorname{mod} 7)$. As much is known about which odd-order abelian groups are R$^*$-sequenceable, we have constructions of R-sequencings for many new families of abelian groups. The construction is generalisable in several directions, leading to a wide array of new R-sequenceable and terraceable non-abelian groups of even order.