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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Translates and multipliers of abelian difference sets


Authors: Robert L. McFarland and Bart F. Rice
Journal: Proc. Amer. Math. Soc. 68 (1978), 375-379
MSC: Primary 05B10
DOI: https://doi.org/10.1090/S0002-9939-1978-0462976-4
MathSciNet review: 0462976
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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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DOI: https://doi.org/10.1090/S0002-9939-1978-0462976-4
Keywords: Difference set, multiplier
Article copyright: © Copyright 1978 American Mathematical Society