具有许多补子群的无限局部有限单群

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2021-09-24 DOI:10.22108/IJGT.2021.129515.1700

M. Ferrara, M. Trombetti

{"title":"具有许多补子群的无限局部有限单群","authors":"M. Ferrara, M. Trombetti","doi":"10.22108/IJGT.2021.129515.1700","DOIUrl":null,"url":null,"abstract":"We prove that the following families of (infinite) groups have complemented subgroup lattice‎: ‎alternating groups‎, ‎finitary symmetric groups‎, ‎Suzuki groups over an infinite locally finite field of characteristic $2$‎, ‎Ree groups over an infinite locally finite field of characteristic~$3$‎. ‎We also show that if the Sylow primary subgroups of a locally finite simple group $G$ have complemented subgroup lattice‎, ‎then this is also the case for $G$‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Infinite Locally Finite Simple Groups with Many Complemented Subgroups\",\"authors\":\"M. Ferrara, M. Trombetti\",\"doi\":\"10.22108/IJGT.2021.129515.1700\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the following families of (infinite) groups have complemented subgroup lattice‎: ‎alternating groups‎, ‎finitary symmetric groups‎, ‎Suzuki groups over an infinite locally finite field of characteristic $2$‎, ‎Ree groups over an infinite locally finite field of characteristic~$3$‎. ‎We also show that if the Sylow primary subgroups of a locally finite simple group $G$ have complemented subgroup lattice‎, ‎then this is also the case for $G$‎.\",\"PeriodicalId\":43007,\"journal\":{\"name\":\"International Journal of Group Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/IJGT.2021.129515.1700\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/IJGT.2021.129515.1700","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

证明了下述(无限)群族具有互补的子群格:特征$2的无限局部有限域上的'交替群'、'有限对称群'、' Suzuki群'和特征$3的无限局部有限域上的' Ree群'。我们还证明了如果局部有限简单群$G$的Sylow初级子群有补子群格，则对于$G$ $也是如此。

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

Infinite Locally Finite Simple Groups with Many Complemented Subgroups

We prove that the following families of (infinite) groups have complemented subgroup lattice‎: ‎alternating groups‎, ‎finitary symmetric groups‎, ‎Suzuki groups over an infinite locally finite field of characteristic $2$‎, ‎Ree groups over an infinite locally finite field of characteristic~$3$‎. ‎We also show that if the Sylow primary subgroups of a locally finite simple group $G$ have complemented subgroup lattice‎, ‎then this is also the case for $G$‎.

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

International Journal of Group Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

30 weeks

期刊介绍： International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.