{"title":"Groups with context-free Diophantine problem","authors":"V. Yankovskiy","doi":"10.46298/jgcc.2021.13.1.7347","DOIUrl":null,"url":null,"abstract":"We find algebraic conditions on a group equivalent to the position of its\nDiophantine problem in the Chomsky Hierarchy. In particular, we prove that a\nfinitely generated group has a context-free Diophantine problem if and only if\nit is finite.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"21 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/jgcc.2021.13.1.7347","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We find algebraic conditions on a group equivalent to the position of its
Diophantine problem in the Chomsky Hierarchy. In particular, we prove that a
finitely generated group has a context-free Diophantine problem if and only if
it is finite.
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