论文标题
非亚伯组中部分差异集的参数的限制
Restrictions on parameters of partial difference sets in nonabelian groups
论文作者
论文摘要
有限组中的部分差异集$ s $满足$ 1 \ notin s $，$ s = s = s^{ - 1} $对应于一个无方向的强烈常规的cayley图$ {\ rm cay}（g，s）$。尽管已经对$ g $是Abelian进行了彻底研究的情况，但是当$ G $是Nonabelian时，结果相对较少。在本文中，我们提供了适用于阿贝尔和非阿贝尔群体的部分差异集的参数的限制，并且在具有非平凡中心的组中特别有效。特别是，这些结果适用于$ p $ groups，我们能够在许多情况下排除部分差异集的存在。
A partial difference set $S$ in a finite group $G$ satisfying $1 \notin S$ and $S = S^{-1}$ corresponds to an undirected strongly regular Cayley graph ${\rm Cay}(G,S)$. While the case when $G$ is abelian has been thoroughly studied, there are comparatively few results when $G$ is nonabelian. In this paper, we provide restrictions on the parameters of a partial difference set that apply to both abelian and nonabelian groups and are especially effective in groups with a nontrivial center. In particular, these results apply to $p$-groups, and we are able to rule out the existence of partial difference sets in many instances.
