{"title":"Growth tightness of quotients by confined subgroups","authors":"Lihuang Ding, Wenyuan Yang","doi":"arxiv-2409.10268","DOIUrl":null,"url":null,"abstract":"In this paper, we establish the growth tightness of the quotient by confined\nsubgroups in groups admitting the statistically convex-cocompact action with\ncontracting elements. The result is sharp in the sense that the actions could\nnot be relaxed with purely exponential growth. Applications to uniformly\nrecurrent subgroups are discussed.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10268","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we establish the growth tightness of the quotient by confined
subgroups in groups admitting the statistically convex-cocompact action with
contracting elements. The result is sharp in the sense that the actions could
not be relaxed with purely exponential growth. Applications to uniformly
recurrent subgroups are discussed.
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