每个a2 -子群H具有H ' =G '的有限p群G

Pub Date : 2023-06-01 DOI:10.1142/s1005386723000238

Dandan Zhang, H. Qu, Yanfeng Luo

{"title":"每个a2 -子群H具有H ' =G '的有限p群G","authors":"Dandan Zhang, H. Qu, Yanfeng Luo","doi":"10.1142/s1005386723000238","DOIUrl":null,"url":null,"abstract":"A finite [Formula: see text]-group [Formula: see text] is called an [Formula: see text]-group if [Formula: see text]is the minimal non-negative integer such that all subgroups of index [Formula: see text] of [Formula: see text] are abelian. The finite [Formula: see text]-groups [Formula: see text] with [Formula: see text] for all [Formula: see text]-subgroups [Formula: see text] of [Formula: see text]are classified completely in this paper. As an application, a problem proposed by Berkovich is solved.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finite p-Groups G with H′=G′ for Each A2-Subgroup H\",\"authors\":\"Dandan Zhang, H. Qu, Yanfeng Luo\",\"doi\":\"10.1142/s1005386723000238\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A finite [Formula: see text]-group [Formula: see text] is called an [Formula: see text]-group if [Formula: see text]is the minimal non-negative integer such that all subgroups of index [Formula: see text] of [Formula: see text] are abelian. The finite [Formula: see text]-groups [Formula: see text] with [Formula: see text] for all [Formula: see text]-subgroups [Formula: see text] of [Formula: see text]are classified completely in this paper. As an application, a problem proposed by Berkovich is solved.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1005386723000238\",\"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/10.1142/s1005386723000238","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

如果[公式:见文]是最小的非负整数，使得[公式:见文]的索引[公式:见文]的所有子群都是阿贝尔的，则有限[公式:见文]群[公式:见文]被称为[公式:见文]群。本文对所有[公式:见文]的[公式:见文]的有限[公式:见文]-群[公式:见文]-子群[公式:见文]进行了完全分类。作为应用，解决了Berkovich提出的一个问题。

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

Finite p-Groups G with H′=G′ for Each A2-Subgroup H

A finite [Formula: see text]-group [Formula: see text] is called an [Formula: see text]-group if [Formula: see text]is the minimal non-negative integer such that all subgroups of index [Formula: see text] of [Formula: see text] are abelian. The finite [Formula: see text]-groups [Formula: see text] with [Formula: see text] for all [Formula: see text]-subgroups [Formula: see text] of [Formula: see text]are classified completely in this paper. As an application, a problem proposed by Berkovich is solved.

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