Abstract
A theorem due to Davis on the existence of Menon difference sets in 2-groups is generalised to non-2-groups. The existence of Menon difference sets in many new non-abelian groups is established.
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J. A. Davis, A generalization of Kraemer's Result on difference sets, J. Comb. Th. (A), Vol. 59 (1992) pp. 187–192.
J. Jedwab, Generalized perfect arrays and Menon difference sets, Designs, Codes and Cryptography, Vol. 2 (1992) pp. 19–68.
I. Kaplansky, Infinite Abelian Groups, University of Michigan Press (1957).
R. E. Kibler, A summary of non-cyclic difference sets, k < 20, J. Comb. Th. (A), Vol. 25 (1978) pp. 62–67.
R. G. Kraemer, Proof of a conjecture on Hadamard 2-groups, J. Comb. Th. (A), Vol. 63 (1993) pp. 1–10.
R. A. Liebler and K. W. Smith, On difference sets in certain 2-groups: Proc. Marshall Hall Conference, Vermont 1990, Coding Theory, Design Theory, Group Theory, Wiley, New York (1991) pp. 195–212.
D. B. Meisner, Families of Menon difference sets: Proceedings of Combinatorics '90, (A. Barlotti et al., eds.), Ann. of Discrete Math., North Holland, 52 (1991) pp. 365–380.
D. B. Meisner, Menon designs and related difference sets, Ph.D. thesis, University of London (1991).
R. J. Turyn, Character sums and difference sets, Pacific J. Math., Vol. 15 (1965) pp. 319–346.
M-y. Xia, Some infinite classes of special Williamson matrices and difference sets, J. Comb. Th. (A), Vol. 61 (1992) pp. 230–242.
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Meisner, D.B. New Classes of Groups Containing Menon Difference Sets. Designs, Codes and Cryptography 8, 319–325 (1996). https://doi.org/10.1023/A:1027355823943
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DOI: https://doi.org/10.1023/A:1027355823943