{"title":"关于循环和阿贝尔有限$p$-群的积($ p$奇数)","authors":"B. McCann","doi":"10.3792/pjaa.94.77","DOIUrl":null,"url":null,"abstract":"For an odd prime p, it is shown that if G 1⁄4 AB is a finite p-group, for subgroups A and B such that A is cyclic and B is abelian of exponent at most p, then kðAÞB E G, where kðAÞ 1⁄4 hg 2 A j g k 1⁄4 1i.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On products of cyclic and abelian finite $p$-groups ($ p$ odd)\",\"authors\":\"B. McCann\",\"doi\":\"10.3792/pjaa.94.77\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For an odd prime p, it is shown that if G 1⁄4 AB is a finite p-group, for subgroups A and B such that A is cyclic and B is abelian of exponent at most p, then kðAÞB E G, where kðAÞ 1⁄4 hg 2 A j g k 1⁄4 1i.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3792/pjaa.94.77\",\"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/10.3792/pjaa.94.77","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
对于奇素数p，证明了如果G 1 / 4 AB是有限p群，对于子群a和B，使得a是循环的，B是幂次的不超过p的，则kðAÞB E G，其中kðAÞ 1 / 4 hg 2 a j G k 1 / 4 1i。
On products of cyclic and abelian finite $p$-groups ($ p$ odd)
For an odd prime p, it is shown that if G 1⁄4 AB is a finite p-group, for subgroups A and B such that A is cyclic and B is abelian of exponent at most p, then kðAÞB E G, where kðAÞ 1⁄4 hg 2 A j g k 1⁄4 1i.
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