论文标题
有限生成的组及其亚组的渐近和纳加塔尺寸
Asymptotic and Assouad-Nagata dimension of finitely generated groups and their subgroups
论文作者
论文摘要
我们证明，对于所有$ k，m，n \ in \ mathbb n \ cup \ {\ infty \} $，带有$ 4 \ leq k \ leq k \ leq m \ leq m \ leq n $，存在有限生成的组$ g $，带有有限生成的子组$ h $ $ g $ g $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ m， $ h $的Assouad-Nagata尺寸为$ n $。这同时回答了渐近维度理论中的两个开放问题。
We prove that for all $k,m,n \in \mathbb N \cup \{\infty\}$ with $4 \leq k \leq m \leq n$, there exists a finitely generated group $G$ with a finitely generated subgroup $H$ such that the asymptotic dimension of $G$ is $k$, the Assouad-Nagata dimension of $G$ is $m$, and the Assouad-Nagata dimension of $H$ is $n$. This simultaneously answers two open questions in asymptotic dimension theory.
