Abstract
It 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
