{"title":"准自凸性检测:算法方面","authors":"Ilya Kapovich","doi":"10.1090/dimacs/025/07","DOIUrl":null,"url":null,"abstract":"The main result of this paper states that for any group $G$ with an automatic structure $L$ with unique representatives one can construct a uniform partial algorithm which detects $L$-rational subgroups and gives their preimages in $L$. This provides a practical, not just theoretical, procedure for solving the occurrence problem for such subgroups.","PeriodicalId":301293,"journal":{"name":"Geometric and Computational Perspectives on Infinite Groups","volume":"18 2","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1995-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"35","resultStr":"{\"title\":\"Detecting quasiconvexity: Algorithmic aspects\",\"authors\":\"Ilya Kapovich\",\"doi\":\"10.1090/dimacs/025/07\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The main result of this paper states that for any group $G$ with an automatic structure $L$ with unique representatives one can construct a uniform partial algorithm which detects $L$-rational subgroups and gives their preimages in $L$. This provides a practical, not just theoretical, procedure for solving the occurrence problem for such subgroups.\",\"PeriodicalId\":301293,\"journal\":{\"name\":\"Geometric and Computational Perspectives on Infinite Groups\",\"volume\":\"18 2\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1995-06-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"35\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometric and Computational Perspectives on Infinite Groups\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/dimacs/025/07\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometric and Computational Perspectives on Infinite Groups","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/dimacs/025/07","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The main result of this paper states that for any group $G$ with an automatic structure $L$ with unique representatives one can construct a uniform partial algorithm which detects $L$-rational subgroups and gives their preimages in $L$. This provides a practical, not just theoretical, procedure for solving the occurrence problem for such subgroups.
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