Work

Soluble groups with no $\mathbb{Z} \wr \mathbb{Z}$ sections

Year: 2018

Type: preprint

Abstract: In this article, we examine how the structure of soluble groups of infinite torsion-free rank with no section isomorphic to the wreath product of two infinite cyclic groups can be analysed. As a corollary, we obtain that if a finitely generated soluble group has a defined Krull dimension and has no sections isomorphic to the wreath product of two infinite cyclic groups then it is a group of finite torsion-free rank. There are further corollaries including applications to return probabilities for random walks. The paper concludes with constructions of examples that can be compared with recent constructions of Brieussel and Zheng.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1805.11497

Authors: Jacoboni, Lison, Kropholler, Peter

Institutions: Université Paris-Saclay, Université Paris-Sud, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques d'Orsay, University of Southampton

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Engineering and Physical Sciences Research Council

Awards: G252364061, G2811597980, Isaac Newton Institute for Mathematical Sciences, G4421442999, G5128091834, Groups, Actions, Metrics, Measures and Ergodic theory, G8238292487

OpenAlex ID: W2806900931

Cites: 10

Cited by:

Related to: 20