Sylow子群数目对有限群可解性的影响

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

C. Anabanti, A. Moretó, M. Zarrin

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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。

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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.

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