{"title":"组 $F\\left(\\frac32\\right)$ 的有限生成","authors":"José Burillo, Marc Felipe","doi":"arxiv-2409.09195","DOIUrl":null,"url":null,"abstract":"In this paper it is proved that the group $F\\left(\\frac32\\right)$, a\nThompson-style group with breaks in $\\mathbb{Z}\\left[\\frac16\\right]$ but whose\nslopes are restricted only to powers of $\\frac32$, is finitely generated, with\na generating set of two elements.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finite generation for the group $F\\\\left(\\\\frac32\\\\right)$\",\"authors\":\"José Burillo, Marc Felipe\",\"doi\":\"arxiv-2409.09195\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper it is proved that the group $F\\\\left(\\\\frac32\\\\right)$, a\\nThompson-style group with breaks in $\\\\mathbb{Z}\\\\left[\\\\frac16\\\\right]$ but whose\\nslopes are restricted only to powers of $\\\\frac32$, is finitely generated, with\\na generating set of two elements.\",\"PeriodicalId\":501037,\"journal\":{\"name\":\"arXiv - MATH - Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-13\",\"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-2409.09195\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09195","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Finite generation for the group $F\left(\frac32\right)$
In this paper it is proved that the group $F\left(\frac32\right)$, a
Thompson-style group with breaks in $\mathbb{Z}\left[\frac16\right]$ but whose
slopes are restricted only to powers of $\frac32$, is finitely generated, with
a generating set of two elements.