Sequencings of Dicyclic Groups II

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 \(n\geq2\), there is a dicyclic group of order \(4n\). It is known that if \(n \geq 3\) 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 \(n\geq 4\) is even and is not twice an odd number, then the dicyclic group of order \(4n\) has a symmetric sequencing.