当前位置: X-MOL 学术J. Topol. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Asymptotic and Assouad–Nagata dimension of finitely generated groups and their subgroups
Journal of Topology ( IF 0.8 ) Pub Date : 2023-12-03 , DOI: 10.1112/topo.12314
Levi Sledd 1
Affiliation  

We prove that for all k , m , n N { } $k,m,n \in \mathbb {N} \cup \lbrace \infty \rbrace$ with 4 k m n $4 \leqslant k \leqslant m \leqslant n$ , there exists a finitely generated group G $G$ with a finitely generated subgroup H $H$ such that asdim ( G ) = k $\operatorname{asdim}(G) = k$ , asdim A N ( G ) = m $\operatorname{asdim}_{\textnormal {AN}}(G) = m$ , and asdim A N ( H ) = n $\operatorname{asdim}_{\textnormal {AN}}(H)=n$ . This simultaneously answers two open questions in asymptotic dimension theory.

中文翻译:

有限生成群及其子群的渐近维数和 Assouad-Nagata 维数

我们证明对于所有人 k , , n ε { 无穷大 } $k,m,n \in \mathbb {N} \cup \lbrace \infty \rbrace$ 4 k n $4 \leqslant k \leqslant m \leqslant n$ ,存在一个有限生成群 G $G$ 具有有限生成的子群 H $H$ 这样 阿斯迪姆 G = k $\operatorname{asdim}(G) = k$ , 阿斯迪姆 A G = $\operatorname{asdim}_{\textnormal {AN}}(G) = m$ , 和 阿斯迪姆 A H = n $\operatorname{asdim}_{\textnormal {AN}}(H)=n$ 。这同时回答了渐进维数理论中的两个悬而未决的问题。
更新日期:2023-12-04
down
wechat
bug