Some construction of group divisible designs with singer groups

✍ Scribed by K.T. Arasu; Alexander Pott

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 451 KB
• Volume: 97
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(91)90419-3

✦ Synopsis

Arasu, K.T. and A. Pott, Some constructions of group divisible designs with Singer groups, Discrete Mathematics 97 (1991) 39-45. Let D be a Menon difference set in a group G with parameters (4u2, 2~' -u, u* -u) and T a divisible difference set (DDS) with parameters (m. n, k, A,, A,) in a group H relative to a subgroup N satisfying what we call property (M): mn = 4(k -&). We provide a recursive construction and show that E = (D, T) U (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 A, = 0 and (M). Finally we give a geometric construction of an infinite family of symmetric divisible designs admitting a Singer group.