Journal article

Publication year: 1991

Pages: 1-8

Journal: Combinatorica

Volume number: 11

Issue number: 1

ISSN: 0209-9683

DOI Link: https://doi.org/10.1007/BF01375467

Publisher: Springer

Abstract: 

In this paper, we shall prove several non-existence results for divisible difference sets, using three approaches: (i) character sum arguments similar to the work of Turyn [25] for ordinary difference sets, (ii) involution arguments and (iii) multipliers in conjunction with results on ordinary difference sets.

Among other results, we show that an abelian affine difference set of odd order s (s not a perfect square) in G can exist only if the Sylow 2-subgroup of G is cyclic. We also obtain a non-existence result for non-cyclic (n, n, n, 1) relative difference sets of odd order n.

Harvard Citation style: ARASU, K., DAVIS, J., JUNGNICKEL, D. and POTT, A. (1991) SOME NONEXISTENCE RESULTS ON DIVISIBLE DIFFERENCE SETS, Combinatorica, 11(1), pp. 1-8. https://doi.org/10.1007/BF01375467

APA Citation style: ARASU, K., DAVIS, J., JUNGNICKEL, D., & POTT, A. (1991). SOME NONEXISTENCE RESULTS ON DIVISIBLE DIFFERENCE SETS. Combinatorica. 11(1), 1-8. https://doi.org/10.1007/BF01375467