{"title":"关于有限无势群的说明","authors":"Nicholas J. Werner","doi":"10.1080/00029890.2024.2379751","DOIUrl":null,"url":null,"abstract":"It is well known that if G is a group and H is a normal subgroup of G of finite index k, then xk∈H for every x∈G. We examine finite groups G with the property that xk∈H for every subgroup H of G, w...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"37 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Note on Finite Nilpotent Groups\",\"authors\":\"Nicholas J. Werner\",\"doi\":\"10.1080/00029890.2024.2379751\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is well known that if G is a group and H is a normal subgroup of G of finite index k, then xk∈H for every x∈G. We examine finite groups G with the property that xk∈H for every subgroup H of G, w...\",\"PeriodicalId\":501497,\"journal\":{\"name\":\"The American Mathematical Monthly\",\"volume\":\"37 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The American Mathematical Monthly\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/00029890.2024.2379751\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The American Mathematical Monthly","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00029890.2024.2379751","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
众所周知，如果 G 是一个群，而 H 是 G 的有限指数 k 的正则子群，则对于每个 x∈G，xk∈H。
It is well known that if G is a group and H is a normal subgroup of G of finite index k, then xk∈H for every x∈G. We examine finite groups G with the property that xk∈H for every subgroup H of G, w...
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