{"title":"满足恒等式$[x^n]的相对自由群的自同构Y] = 1$","authors":"Sh. A. Stepanyan","doi":"10.46991/pysu:a/2017.51.2.196","DOIUrl":null,"url":null,"abstract":"We prove that if an automorphism j of the relatively free group of the group variety, defined by the identity relation $[x^n; y] = 1$, acts identically on its center, then j has either infinite or odd order, where $n\\geq 665$ is an arbitrary odd number.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"162 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"ON AUTOMORPHISMS OF THE RELATIVELY FREE GROUPS SATISFYING THE IDENTITY $[x^n; y] = 1$\",\"authors\":\"Sh. A. Stepanyan\",\"doi\":\"10.46991/pysu:a/2017.51.2.196\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that if an automorphism j of the relatively free group of the group variety, defined by the identity relation $[x^n; y] = 1$, acts identically on its center, then j has either infinite or odd order, where $n\\\\geq 665$ is an arbitrary odd number.\",\"PeriodicalId\":21146,\"journal\":{\"name\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"volume\":\"162 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46991/pysu:a/2017.51.2.196\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the YSU A: Physical and Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46991/pysu:a/2017.51.2.196","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON AUTOMORPHISMS OF THE RELATIVELY FREE GROUPS SATISFYING THE IDENTITY $[x^n; y] = 1$
We prove that if an automorphism j of the relatively free group of the group variety, defined by the identity relation $[x^n; y] = 1$, acts identically on its center, then j has either infinite or odd order, where $n\geq 665$ is an arbitrary odd number.
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