{"title":"关于换元具有质幂阶的可解群","authors":"Mateus Figueiredo, Pavel Shumyatsky","doi":"arxiv-2408.01974","DOIUrl":null,"url":null,"abstract":"The article deals with finite groups in which commutators have prime power\norder (CPPO-groups). We show that if G is a soluble CPPO-group, then the order\nof the commutator subgroup G' is divisible by at most two primes.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On soluble groups in which commutators have prime power order\",\"authors\":\"Mateus Figueiredo, Pavel Shumyatsky\",\"doi\":\"arxiv-2408.01974\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The article deals with finite groups in which commutators have prime power\\norder (CPPO-groups). We show that if G is a soluble CPPO-group, then the order\\nof the commutator subgroup G' is divisible by at most two primes.\",\"PeriodicalId\":501037,\"journal\":{\"name\":\"arXiv - MATH - Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.01974\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.01974","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
文章涉及换元具有素幂阶的有限群(CPPO-群)。我们证明,如果 G 是一个可溶的 CPPO 群,那么换元子群 G' 的阶最多可被两个素数整除。
On soluble groups in which commutators have prime power order
The article deals with finite groups in which commutators have prime power
order (CPPO-groups). We show that if G is a soluble CPPO-group, then the order
of the commutator subgroup G' is divisible by at most two primes.