On orthogonal orthomorphisms of cyclic and non-abelian groups. II
✍ Scribed by Anthony B. Evans
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 187 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1063-8539
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✦ Synopsis
Abstract
We construct sets of three pairwise orthogonal orthomorphisms of Z~3__n__~, n not divisible by either 2 or 3, n ≠ 7, 17. Combined with results in the literature, this reduces the problem of determining for which v, there exist three pairwise orthogonal orthomorphisms of Z~v~ to the case v = 9__p__, p > 3 a prime. This yields new lower bounds for the number of pairwise orthogonal orthomorphisms of classes of dihedral groups of doubly even order, and classes of linear groups. These results also find application in the construction of Z‐cyclic triplewhist tournaments. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 195–209, 2007