Sylow子群数目对有限群可解性的影响

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2021-01-25 DOI:10.5802/CRMATH.146

C. Anabanti, A. Moretó, M. Zarrin

{"title":"Sylow子群数目对有限群可解性的影响","authors":"C. Anabanti, A. Moretó, M. Zarrin","doi":"10.5802/CRMATH.146","DOIUrl":null,"url":null,"abstract":"Let G be a finite group. We prove that if the number of Sylow 3-subgroups of G is at most 7 and the number of Sylow 5-subgroups of G is at most 1455, then G is solvable. This is a strong form of a recent conjecture of Robati. 2020 Mathematics Subject Classification. 20D10, 20D20, 20F16, 20F19. Funding. The first author is supported by both TU Graz (R-1501000001) and partial funding from the Austrian Science Fund (FWF): P30934–N35, F05503, F05510. He is also at the University of Nigeria, Nsukka (UNN). The research of the second author is supported by Ministerio de Ciencia e Innovación PID−2019−103854GB−100, Generalitat Valenciana AICO/2020/298 and FEDER funds. Manuscript received 4th October 2020, revised and accepted 5th November 2020.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":"84 1","pages":"1227-1230"},"PeriodicalIF":0.8000,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Influence of the number of Sylow subgroups on solvability of finite groups\",\"authors\":\"C. Anabanti, A. Moretó, M. Zarrin\",\"doi\":\"10.5802/CRMATH.146\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be a finite group. We prove that if the number of Sylow 3-subgroups of G is at most 7 and the number of Sylow 5-subgroups of G is at most 1455, then G is solvable. This is a strong form of a recent conjecture of Robati. 2020 Mathematics Subject Classification. 20D10, 20D20, 20F16, 20F19. Funding. The first author is supported by both TU Graz (R-1501000001) and partial funding from the Austrian Science Fund (FWF): P30934–N35, F05503, F05510. He is also at the University of Nigeria, Nsukka (UNN). The research of the second author is supported by Ministerio de Ciencia e Innovación PID−2019−103854GB−100, Generalitat Valenciana AICO/2020/298 and FEDER funds. Manuscript received 4th October 2020, revised and accepted 5th November 2020.\",\"PeriodicalId\":10620,\"journal\":{\"name\":\"Comptes Rendus Mathematique\",\"volume\":\"84 1\",\"pages\":\"1227-1230\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-01-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus Mathematique\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/CRMATH.146\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus Mathematique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/CRMATH.146","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设G是一个有限群。证明了如果G的Sylow 3-子群的个数不大于7,G的Sylow 5-子群的个数不大于1455，则G是可解的。这是Robati最近猜想的一种强形式。2020数学学科分类。20D10, 20D20, 20F16, 20F19。资金。第一作者得到格拉茨工业大学(R-1501000001)和奥地利科学基金(FWF)的部分资助:P30934-N35, F05503, F05510。他还在尼日利亚恩苏卡大学(UNN)工作。第二作者的研究得到了Ministerio de Ciencia e Innovación PID−2019−103854GB−100、Generalitat Valenciana AICO/2020/298和federer基金的支持。2020年10月4日收稿，2020年11月5日修改并验收。

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

Influence of the number of Sylow subgroups on solvability of finite groups

Let G be a finite group. We prove that if the number of Sylow 3-subgroups of G is at most 7 and the number of Sylow 5-subgroups of G is at most 1455, then G is solvable. This is a strong form of a recent conjecture of Robati. 2020 Mathematics Subject Classification. 20D10, 20D20, 20F16, 20F19. Funding. The first author is supported by both TU Graz (R-1501000001) and partial funding from the Austrian Science Fund (FWF): P30934–N35, F05503, F05510. He is also at the University of Nigeria, Nsukka (UNN). The research of the second author is supported by Ministerio de Ciencia e Innovación PID−2019−103854GB−100, Generalitat Valenciana AICO/2020/298 and FEDER funds. Manuscript received 4th October 2020, revised and accepted 5th November 2020.

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

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.