{"title":"On a finite state representation of GL(n,Z)","authors":"A. Oliynyk, V. Prokhorchuk","doi":"10.12958/adm2158","DOIUrl":null,"url":null,"abstract":"It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups GL(n,Z). The number of states of automorphisms that correspond to elementary matrices i computed. Using the representation of GL(2,Z) over an alphabet of size 4 a finite state representation of the freegroup of rank 2 over binary alphabet is constructed.","PeriodicalId":364397,"journal":{"name":"Algebra and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm2158","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
It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups GL(n,Z). The number of states of automorphisms that correspond to elementary matrices i computed. Using the representation of GL(2,Z) over an alphabet of size 4 a finite state representation of the freegroup of rank 2 over binary alphabet is constructed.