Let D be a (v, k, lambda)-difference set in a group G. Assume that G has a normal subgroup N such that G/N is cyclic or nearly cyclic. Under the self-conjugacy assumption on exp(G/N), we shall give bounds on N and lambda. The theorem is applicable to a wider variety of parameters for groups, not necessarily abelian. These bounds exclude a (96, 20, 4)-difference set in Z/4Z x Z/8Z x Z/3Z or Z/2Z x Z/2Z x Z/8Z x Z/3Z, which were recently proved by Arasu et al. [1996, K. T. Arasu, J. A. Davis, J. Jedwab, S. L. Ma, and R. L. McFarland, in "Exponent Bounds for a Family of Abelian Difference Sets" (K. T. Arasu, J. F. Dillon, K. Harada, S. K. Sehgal, and R. L. Solomon, Eds.), pp. 129-143. DeGruyter Verlag, Berlin/New York]. (C) 1998 Academic Press. [References: 7]
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机译：令D为组G中的一个（v，k，λ）差集。假设G具有一个正常的子组N，使得G / N是循环的或接近循环的。在exp（G / N）的自共轭假设下，我们将给 N 和lambda给出边界。该定理适用于群体的各种参数，不一定是阿贝尔的。这些界限不包括Z / 4Z x Z / 8Z x Z / 3Z或Z / 2Z x Z / 2Z x Z / 8Z x Z / 3Z中的（96、20、4）差集，最近由Arasu等人证明了这一点等[1996年，KT Arasu，JA Davis，J。Jedwab，SL Ma和RL McFarland，在“ Abelian差异集家庭的指数界”（KT Arasu，JF Dillon，K。Harada，SK Sehgal和RL Solomon，编，第129-143页。 DeGruyter Verlag，柏林/纽约]。 （C）1998年学术出版社。 [参考：7]
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