{"title":"Abelianization of the Cartwright-Steger lattice","authors":"Guy Blachar, Orit Sela–Ben-David, U. Vishne","doi":"10.12958/adm1966","DOIUrl":null,"url":null,"abstract":"The Cartwright-Steger lattice is a group whose Cayley graph can be identified with the Bruhat-Tits building of PGLd over a local field of positive characteristic. We give a lower bound on the abelianization of this lattice, and report that the bound is tight in all computationally accessible cases.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra & Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm1966","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
The Cartwright-Steger lattice is a group whose Cayley graph can be identified with the Bruhat-Tits building of PGLd over a local field of positive characteristic. We give a lower bound on the abelianization of this lattice, and report that the bound is tight in all computationally accessible cases.
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