{"title":"不可分解局部有限群的密度","authors":"S. Shelah","doi":"10.4171/rsmup/68","DOIUrl":null,"url":null,"abstract":"We prove that for any locally finite group there is an extension of the same cardinality which is indecomposable for almost all regular cardinals smaller than its cardinality. Note that a group G is called θ-indecomposable when for every increasing sequence 〈Gi : i < θ〉 of subgroups with union G there is i < θ such that G = Gi. Mathematics Subject Classification (2010). Primary:20A10,03C60","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"69 1","pages":"253-270"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Density of indecomposable locally finite groups\",\"authors\":\"S. Shelah\",\"doi\":\"10.4171/rsmup/68\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that for any locally finite group there is an extension of the same cardinality which is indecomposable for almost all regular cardinals smaller than its cardinality. Note that a group G is called θ-indecomposable when for every increasing sequence 〈Gi : i < θ〉 of subgroups with union G there is i < θ such that G = Gi. Mathematics Subject Classification (2010). Primary:20A10,03C60\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"69 1\",\"pages\":\"253-270\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/rsmup/68\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/68","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that for any locally finite group there is an extension of the same cardinality which is indecomposable for almost all regular cardinals smaller than its cardinality. Note that a group G is called θ-indecomposable when for every increasing sequence 〈Gi : i < θ〉 of subgroups with union G there is i < θ such that G = Gi. Mathematics Subject Classification (2010). Primary:20A10,03C60
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