{"title":"$mathcal{C}$氦共轭可分离群和花环积","authors":"Alexander Bishop, Michal Ferov, Mark Pengitore","doi":"arxiv-2409.06200","DOIUrl":null,"url":null,"abstract":"We provide a necessary and sufficient condition for the restricted wreath\nproduct $A\\wr B$ to be $\\mathcal{C}$-hereditarily conjugacy separable where\n$\\mathcal{C}$ is an extension-closed pseudo-variety of finite groups. Moreover,\nwe prove that the Grigorchuk group is 2-hereditarily conjugacy separable.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":"71 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$\\\\mathcal{C}$-Hereditarily conjugacy separable groups and wreath products\",\"authors\":\"Alexander Bishop, Michal Ferov, Mark Pengitore\",\"doi\":\"arxiv-2409.06200\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide a necessary and sufficient condition for the restricted wreath\\nproduct $A\\\\wr B$ to be $\\\\mathcal{C}$-hereditarily conjugacy separable where\\n$\\\\mathcal{C}$ is an extension-closed pseudo-variety of finite groups. Moreover,\\nwe prove that the Grigorchuk group is 2-hereditarily conjugacy separable.\",\"PeriodicalId\":501037,\"journal\":{\"name\":\"arXiv - MATH - Group Theory\",\"volume\":\"71 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"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-2409.06200\",\"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-2409.06200","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
$\mathcal{C}$-Hereditarily conjugacy separable groups and wreath products
We provide a necessary and sufficient condition for the restricted wreath
product $A\wr B$ to be $\mathcal{C}$-hereditarily conjugacy separable where
$\mathcal{C}$ is an extension-closed pseudo-variety of finite groups. Moreover,
we prove that the Grigorchuk group is 2-hereditarily conjugacy separable.
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