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A representation theorem and Z-cyclic whist tournaments

✍ Scribed by Norman J. Finizio

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 538 KB
Volume: 3
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180030206

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✦ Synopsis

Let E denote the group of units (i.e., the reduce set of residues) in the ring Z3p,,n. Here we consider q,p to be primes, q = 3 (mod 4), q 2 7, p = 1 (mod 4). Let W denote a common primitive root of 3, q, and p 2 . If H denotes the (normal) subgroup of E that is generated by {-1, W } , we show that the factor group E / H is cyclic by demonstrating the existence of an element x in E such that the coset X H has order equal to IE/HI. This order is given by gcd(p"-'(p -1 ) , q -1). This representation of E / H is exploited via an appropriate construction to produce Z-cyclic whist tournaments for 3qp" players. Consequently these results extend those of an early study of Wh(3qp") that was restricted to gcd(p"-'(p -I), q -1) = 2. 0 1995 John Wiley & Sons, he.

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