关于换元具有质幂阶的可解群

arXiv - MATH - Group Theory Pub Date : 2024-08-04 DOI:arxiv-2408.01974

Mateus Figueiredo, Pavel Shumyatsky

{"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":"6 1","pages":""},"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\":\"6 1\",\"pages\":\"\"},\"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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

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

来源期刊

arXiv - MATH - Group Theory

自引率

0.00%

发文量