{"title":"$ \\operatorname{Lim}(N) $中的局部有限子群","authors":"N. M. Suchkov, A. A. Shlepkin","doi":"10.1134/s0037446623060150","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\( G \\)</span> be the group of all limited permutations of the naturals <span>\\( N \\)</span>.\nWe prove that every countable locally finite group is isomorphic to a subgroup in <span>\\( G \\)</span>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Locally Finite Subgroups in $ \\\\operatorname{Lim}(N) $\",\"authors\":\"N. M. Suchkov, A. A. Shlepkin\",\"doi\":\"10.1134/s0037446623060150\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <span>\\\\( G \\\\)</span> be the group of all limited permutations of the naturals <span>\\\\( N \\\\)</span>.\\nWe prove that every countable locally finite group is isomorphic to a subgroup in <span>\\\\( G \\\\)</span>.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0037446623060150\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0037446623060150","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设\( G \)为自然界中所有有限置换的群\( N \),证明了每个可数的局部有限群与\( G \)中的子群同构。
On Locally Finite Subgroups in $ \operatorname{Lim}(N) $
Let \( G \) be the group of all limited permutations of the naturals \( N \).
We prove that every countable locally finite group is isomorphic to a subgroup in \( G \).