Asymptotic and Assouad–Nagata dimension of finitely generated groups and their subgroups

IF 0.8 2区数学 Q2 MATHEMATICS Journal of Topology Pub Date : 2023-12-03 DOI:10.1112/topo.12314

Levi Sledd

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引用次数: 1

Abstract

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

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有限生成群及其子群的渐近维数和副长维数

我们向所有k m证明，n ∈ N ∪ { ∞ } $ k, m, n在杯赛mathbb {n} \ \ lbrace infty \ rbrace $ 一起散步 4 ⩽ k ⩽ m ⩽ n $ 4 \ leqslant k leqslant m \ leqslant n $ ,在一个有限的G美元集团中存在着一个有限的G美元子集团H美元H这样的asdim (G)asdim AN (G)和asdim AN (H)这实际上是两个在异步维度问题的答案。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.