Please use this identifier to cite or link to this item:
|Title:||Abelian divisible difference sets with multiplier -1||Authors:||Leung, K.H.
|Issue Date:||Jan-1992||Citation:||Leung, K.H.,Ma, S.L.,Tan, V. (1992-01). Abelian divisible difference sets with multiplier -1. Journal of Combinatorial Theory, Series A 59 (1) : 51-72. ScholarBank@NUS Repository.||Abstract:||We investigate (m, n, k, λ1, λ2)-divisible difference sets in an abelian group admitting -1 as a multiplier. For the reversible case, we show that this assumption implies severe restrictions on the structure of divisible difference sets. In particular, if (λ1 - λ2)n + k - λ1 is not a square, we prove that all the corresponding divisible difference sets can be constructed by using certain partial difference sets. Also, we determine the structure of reversible divisible difference sets if a Sylow subgroup of G is cyclic. As a consequence, we completely characterize all reversible divisible difference sets in cyclic groups. Finally, the case that -1 is a weak multiplier is studied and restrictions on the parameters are obtained. In fact, we show that n must be a power of 2. © 1992.||Source Title:||Journal of Combinatorial Theory, Series A||URI:||http://scholarbank.nus.edu.sg/handle/10635/102790||ISSN:||00973165|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Nov 24, 2022
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.