A major conjecture on the existence of abelian skew Hadamard difference sets is: if an abelian group $G$ contains a skew Hadamard difference set, then $G$ must be elementary abelian. This conjecture remains open in general. In this paper, we give a recursive construction for skew Hadamard difference sets in abelian (not necessarily elementary abelian) groups. The new construction can be considered as a result on the aforementioned conjecture: if there exists a counterexample to the conjecture, then there exist infinitely many counterexamples to it.
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机译：关于阿贝尔偏斜的哈马德差异集存在的主要猜想是：如果abelian组$ g $包含一个偏斜的hadamard差异集，那么$ g $必须是初级的abelian。这个猜想一般仍然开放。在本文中，我们为阿比埃斯（不一定是基本的雅利安）群体中的偏斜Hadamard差异集提供递归结构。新的结构可以考虑在上述猜想上的结果：如果猜想存在反例，那么它对它有无限的体重夹。
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