{"title":"Regular maps from the lamplighter to metabelian groups","authors":"Antoine Gournay, Corentin Le Coz","doi":"10.1112/blms.13142","DOIUrl":null,"url":null,"abstract":"<p>We prove that the lamplighter group admits an injective Lipschitz map to any finitely generated metabelian group that is not virtually nilpotent. This implies that finitely generated metabelian groups satisfy the “analytically thin/analytically thick” dichotomy recently introduced by Hume, Mackay, and Tessera.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3428-3433"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13142","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that the lamplighter group admits an injective Lipschitz map to any finitely generated metabelian group that is not virtually nilpotent. This implies that finitely generated metabelian groups satisfy the “analytically thin/analytically thick” dichotomy recently introduced by Hume, Mackay, and Tessera.
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