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The Multiplier Theorem for Difference Sets

Published online by Cambridge University Press:  20 November 2018

Richard J. Turyn
Richard J. Turyn*
Affiliation:
Sylvania Electric, Waltham, Massachusetts
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In a recent paper (5) Newman proved the following theorem: if D is a difference set in a cyclic group G and n = q is prime, then q is a multiplier of D. If n = 2q and (v, 7) = 1, then q is a multiplier of D. The purpose of this note is to point out that a stronger statement than the first part was proved in (1), to remove the restriction (v, 7) = 1 in the second part, and to give again and make some comments about the proof of the theorem which asserts that a prime divisor of n is a multiplier of D if prime to v.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 386 - 388
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Hall, Marshall Jr., A survey of difference sets, Proc. Am. Math. Soc, 7 (1956), 975–986.Google Scholar
2. Lehmer, Emma, Period equations applied to difference sets, Proc. Am. Math. Soc, 6 (1955), 433–442.Google Scholar
3. Mann, H. B., Balanced incomplete block designs and abelian difference sets, Boeing Scientific Research Laboratories (August, 1962).Google Scholar
4. Menon, P. K., Difference sets in abelian groups, Proc. Am. Math. Soc, 11 (1960), 368–376.Google Scholar
5. Newman, Morris, Multipliers of difference sets, Can. J. Math., 15 (1963), 121–124.Google Scholar