{"title":"关于自由群单态检验元素的说明","authors":"Dongxiao Zhao, Qiang Zhang","doi":"arxiv-2408.13449","DOIUrl":null,"url":null,"abstract":"A word in a group is called a test element if any endomorphism fixing it is\nnecessarily an automorphism. In this note, we give a sufficient condition in\ngeometry to construct test elements for monomorphisms of a free group, by using\nthe Whitehead graph and the action of the free group on its Cayley graph.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on test elements for monomorphisms of free groups\",\"authors\":\"Dongxiao Zhao, Qiang Zhang\",\"doi\":\"arxiv-2408.13449\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A word in a group is called a test element if any endomorphism fixing it is\\nnecessarily an automorphism. In this note, we give a sufficient condition in\\ngeometry to construct test elements for monomorphisms of a free group, by using\\nthe Whitehead graph and the action of the free group on its Cayley graph.\",\"PeriodicalId\":501037,\"journal\":{\"name\":\"arXiv - MATH - Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.13449\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.13449","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A note on test elements for monomorphisms of free groups
A word in a group is called a test element if any endomorphism fixing it is
necessarily an automorphism. In this note, we give a sufficient condition in
geometry to construct test elements for monomorphisms of a free group, by using
the Whitehead graph and the action of the free group on its Cayley graph.
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