Journal article

Publication year: 1991

Pages: 39-45

Journal: Discrete Mathematics

Volume number: 97

Issue number: 1-3

ISSN: 0012-365X

Open access status: Bronze

DOI Link: https://doi.org/10.1016/0012-365X(91)90419-3

Publisher: Elsevier

Abstract: 
Let D be a Menon difference set in a group G with parameters (4u2, 2u2 - u, u2 - u) and T a divisible difference set (DDS) with parameters (m, n, k, lambda-1, lambda-2) in a group H relative to a subgroup N satisfying what we call property (M): mn = 4(k - lambda-2). We provide a recursive construction and show that E = (D, T) or (G \ D, H \ T) is a DDS in G + H relative to N. Furthermore, E also satisfies property (M). Our proof shows that this construction will work only when T has property (M). We also provide several series of examples of DDS's admitting - 1 as a multiplier. We characterize the DDS's with lambda-1 = 0 and (M). Finally we give a geometric construction of an infinite family of symmetric divisible designs admitting a Singer group.

Harvard Citation style: ARASU, K. and POTT, A. (1991) SOME CONSTRUCTIONS OF GROUP DIVISIBLE DESIGNS WITH SINGER GROUPS, Discrete Mathematics, 97(1-3), pp. 39-45. https://doi.org/10.1016/0012-365X(91)90419-3

APA Citation style: ARASU, K., & POTT, A. (1991). SOME CONSTRUCTIONS OF GROUP DIVISIBLE DESIGNS WITH SINGER GROUPS. Discrete Mathematics. 97(1-3), 39-45. https://doi.org/10.1016/0012-365X(91)90419-3