A partial difference set $S$ in a finite group $G$ satisfying $1 \notin S$ and $S = S^{-1}$ corresponds to an undirected 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.

中文翻译：

---

非阿贝尔群中偏差分集参数的限制

满足$1 \notin S$ 和$S = S^{-1}$ 的有限群$G$ 中的部分差分集$S$ 对应于无向凯莱图${\rm Cay}(G,S)$。虽然已经彻底研究了 $G$ 是阿贝尔的情况，但当 $G$ 是非阿贝尔时，结果相对较少。在本文中，我们提供了对适用于阿贝尔群和非阿贝尔群的偏差分集参数的限制，并且在具有非平凡中心的群中尤其有效。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。