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On orthogonal orthomorphisms of cyclic and non‐abelian groups. II
Author(s) -
Evans Anthony B.
Publication year - 2007
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20138
Subject(s) - mathematics , dihedral group , combinatorics , pairwise comparison , abelian group , prime (order theory) , cyclic group , order (exchange) , group (periodic table) , orthogonal array , dihedral angle , statistics , taguchi methods , hydrogen bond , chemistry , organic chemistry , finance , molecule , economics
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