Let D be an affine difference set of order n in an abelian group G relative to a subgroup N. Set [(H)tilde]{tilde{H}} = H {1, ω}, where H = G/N and w = Õs Î Hs{omega=prod_{sigmain H}sigma} . Using D we define a two-to-one map g from [(H)tilde]{tilde{H}} to N. The map g satisfies g(σ m ) = g(σ) m and g(σ) = g(σ −1) for any multiplier m of D and any element σ ∈ [(H)tilde]{tilde{H}} . As applications, we present some results which give a restriction on the possible order n and the group theoretic structure of G/N.
展开▼
机译：令D为相对于子组N的阿贝尔群G中阶n的仿射差集。设置[（H）tilde] {tilde {H}} = H {1，ω}，其中H = G / N和w = sub sÎH s {omega = prod_ {sigmain H} sigma}。使用D定义从[（H）tilde] {tilde {H}}到N的一对一映射g。该映射g满足g（σ m ）= g（σ）< sup> m 和g（σ）= g（σ −1 ）对于D的任何乘数m和任何元素σ∈[（H）tilde] {tilde {H}}。作为应用，我们给出一些结果，这些结果限制了可能的阶数n和G / N的群论结构。
展开▼
