论 $ \operatorname{Lim}(N) $ 中的正则子群

Pub Date : 2024-05-29 DOI:10.1134/s0037446624030121

N. M. Suchkov, A. A. Shlepkin

{"title":"论 $ \\operatorname{Lim}(N) $ 中的正则子群","authors":"N. M. Suchkov, A. A. Shlepkin","doi":"10.1134/s0037446624030121","DOIUrl":null,"url":null,"abstract":"Let \$ G \$ be the group of all limited permutations of the set of naturals.\nWe prove that every countable locally finite group is isomorphic to some regular\nsubgroup of \$ G \$. Also, if a regular subgroup \$ H \$ of \$ G \$ contains an element\nof infinite order then \$ H \$ has a normal infinite cyclic subgroup of finite index.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Regular Subgroups in $ \\\\operatorname{Lim}(N) $\",\"authors\":\"N. M. Suchkov, A. A. Shlepkin\",\"doi\":\"10.1134/s0037446624030121\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let \\\$ G \\\$ be the group of all limited permutations of the set of naturals.\\nWe prove that every countable locally finite group is isomorphic to some regular\\nsubgroup of \\\$ G \\\$. Also, if a regular subgroup \\\$ H \\\$ of \\\$ G \\\$ contains an element\\nof infinite order then \\\$ H \\\$ has a normal infinite cyclic subgroup of finite index.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-29\",\"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/s0037446624030121\",\"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/s0037446624030121","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

我们证明每个可数局部有限群都与$ G$ 的某个正则子群同构。同时，如果 G 的正则子群 H 包含一个无限阶元素，那么 H 有一个有限索引的正则无限循环子群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

On Regular Subgroups in $ \operatorname{Lim}(N) $

Let $ G $ be the group of all limited permutations of the set of naturals. We prove that every countable locally finite group is isomorphic to some regular subgroup of $ G $. Also, if a regular subgroup $ H $ of $ G $ contains an element of infinite order then $ H $ has a normal infinite cyclic subgroup of finite index.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助