Abstract
In this paper, we use number theoretic methods to study multipliers and numerical multiplier groups of difference sets. We obtain a relation between the decomposition group of a prime divisor of the order of a difference set and the numerical multiplier group, this gives rise to some results concerning the numerical multiplier groups of difference sets. Also we give two characterizations of strong multipliers of a subset in an abelian group which have some applications in difference sets.
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Arasu, K.T.: On Wilbrink’s theorem, J. Comb. Theory (A)44, 156–158 (1987)
Arasu, K.T., Xiang, Q.: Multiplier Theorems, submitted
Baumert, L.D.: Cyclic difference sets, Lect. Notes Math. Vol. 182, Springer, New York, (1971)
Ho, C.Y.: On bounds for groups of multipliers of planar difference sets, J. Algebra148, 325–336 (1992)
Jacobson, N.: Basic Algebra 2, San Francisco, W.H. Freeman, (1974)
Jungnickel, D.: Difference Sets, A Survey, Contemporary Design Theory: A Collection Of Surveys, Edited by J.H. Dinitz and D.R. Stinson, (1992)
Lander, E.S.: Symmetric Designs, An Algebraic Approach, Cambridge University Press, Cambridge, (1983)
Ma, S.L.: Polynomial Addition Sets, Ph.D Thesis, University of Hong Kong, (1985)
Marcus, L: Number Fields, Springer, 1977
McFarland, R.L., Rice, B.F.: Translates and multipliers of abelian difference sets, Proc. Amer. Math. Soc.68, 375–379 (1978)
Turyn, R.J.: Character sums and difference sets, Pacific J. Math.15, 319–346 (1965)
Weiss, E.: Algebraic Number Theory, New York, McGraw Hill, (1963)
Xiang, Q., Chen, Y.Q.: On the size of the multiplier groups of cyclic difference sets, J. Comb. Theory, (A) (to be published)
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Xiang, Q. Some results on multipliers and numerical multiplier groups of difference sets. Graphs and Combinatorics 10, 293–304 (1994). https://doi.org/10.1007/BF02986679
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DOI: https://doi.org/10.1007/BF02986679