Translates and multipliers of abelian difference sets

McFarland, Robert L.; Rice, Bart F.

doi:10.1090/S0002-9939-1978-0462976-4

Translates and multipliers of abelian difference sets
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by Robert L. McFarland and Bart F. Rice PDF

Proc. Amer. Math. Soc. 68 (1978), 375-379 Request permission

Abstract:

It is shown that every abelian difference set has a translate which is fixed by all numerical multipliers. If an abelian difference set in a group of order v has numerical multipliers ${t_1}, \ldots ,{t_m}$ which satisfy $\gcd ({t_1} - 1, \ldots ,{t_m} - 1,v) = 1$, then there is a unique translate which is fixed by all multipliers.

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