{"title":"关于 GL(n,Z) 的有限状态表示","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":"{\"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}","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}
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.
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