中心化子格的断点
Breaking points in centralizer lattices
摘要：
本文证明了群$G$的中心化子格${\mathfrak C}(G)$不能写成两个真区间的并.特别地，由此得出${\mathfrak C}(G)$没有断裂点。作为一个应用，我们证明了广义四元数$2$ -群是不可能的。
英文摘要：
In this note, we prove that the centralizer lattice ${\mathfrak C}(G)$ of a group $G$ cannot be written as a union of two proper intervals. In particular, it follows that ${\mathfrak C}(G)$ has no breaking point. As an application, we show that the generalized quaternion $2$-groups are not capable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
