{"title":"Friends and relatives of BS(1,2)","authors":"C. F. Miller III","doi":"10.1515/gcc-2014-0006","DOIUrl":null,"url":null,"abstract":"Algorithms, constructions and examples are of central interest in combinatorial and geometric group theory. Teaching experience and, more recently, preparing a historical essay have led me to think the familiar group BS(1, 2) is an example of fundamental importance. The purpose of this note is to make a case for this point of view.We recall several interesting constructions and important examples of groups related to BS(1, 2), and indicate why certain of these groups played a key role in showing the word problem for nitely presented groups is unsolvable.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"32 1","pages":"73 - 80"},"PeriodicalIF":0.1000,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc-2014-0006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Algorithms, constructions and examples are of central interest in combinatorial and geometric group theory. Teaching experience and, more recently, preparing a historical essay have led me to think the familiar group BS(1, 2) is an example of fundamental importance. The purpose of this note is to make a case for this point of view.We recall several interesting constructions and important examples of groups related to BS(1, 2), and indicate why certain of these groups played a key role in showing the word problem for nitely presented groups is unsolvable.