Breaking points in centralizer lattices. (arXiv:1802.03554v1 [math.GR])

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. 查看全文>>