Sequencings of Dicyclic Groups II

Abstract

Recent examples of perfect 1-factorizations arising from dicyclic groups have led to the question of whether or not dicyclic groups have symmetric sequencings. For every positive integer $n\ge 2$, there is a dicyclic group of order $4n$. It is known that if $n\ge 3$ is odd, then the dicyclic group of order $4n$ has a symmetric sequencing. In this paper, a new proof is given for the odd case; a consequence being that in this situation sequencings abound. A generalization of the original proof is exploited to show that if $n\ge 4$ is even and is not twice an odd number, then the dicyclic group of order $4n$ has a symmetric sequencing.