A product theorem for 2-sequencings

AbstractIt is shown that if a finite group G of odd order has what is called a starter-translate 2-sequencing and a finite group H has a 2-sequencing, then the group G × H has a 2-sequencing. This generalizes a theorem of Bailey. Special cases of this result can be applied to various questions involving sequencings of groups. For example, Keedwell has exhibited a class of non-Abelian groups of odd order that have sequencings. Some of these sequencings are starter-translate sequencings and it follows that the collection of odd positive integer orders for which there is a known non-Abelian sequenceable group (and hence a complete Latin square) can be substantially enlarged. New classes of non-Abelian groups with a unique element of order two are shown to have symmetric sequencings