## 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

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 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.