无限对称群的最大子群

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-29 DOI:10.1017/s0004972723001375

SUZANA MENDES-GONÇALVES, R. P. SULLIVAN

{"title":"无限对称群的最大子群","authors":"SUZANA MENDES-GONÇALVES, R. P. SULLIVAN","doi":"10.1017/s0004972723001375","DOIUrl":null,"url":null,"abstract":"Brazil et al. [‘Maximal subgroups of infinite symmetric groups’, Proc. Lond. Math. Soc. (3)68(1) (1994), 77–111] provided a new family of maximal subgroups of the symmetric group $G(X)$ defined on an infinite set X. It is easy to see that, in this case, $G(X)$ contains subsemigroups that are not groups, but nothing is known about nongroup maximal subsemigroups of $G(X)$ . We provide infinitely many examples of such semigroups.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"MAXIMAL SUBSEMIGROUPS OF INFINITE SYMMETRIC GROUPS\",\"authors\":\"SUZANA MENDES-GONÇALVES, R. P. SULLIVAN\",\"doi\":\"10.1017/s0004972723001375\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Brazil et al. [‘Maximal subgroups of infinite symmetric groups’, Proc. Lond. Math. Soc. (3)68(1) (1994), 77–111] provided a new family of maximal subgroups of the symmetric group $G(X)$ defined on an infinite set X. It is easy to see that, in this case, $G(X)$ contains subsemigroups that are not groups, but nothing is known about nongroup maximal subsemigroups of $G(X)$ . We provide infinitely many examples of such semigroups.\",\"PeriodicalId\":50720,\"journal\":{\"name\":\"Bulletin of the Australian Mathematical Society\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-01-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Australian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0004972723001375\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Australian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0004972723001375","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

Brazil et al. ['Maximal subgroups of infinite symmetric groups', Proc.Lond.Math.(3)68(1) (1994), 77-111] 提供了定义在无限集 X 上的对称群 $G(X)$ 的最大子群的新族。我们提供了无限多此类半群的例子。

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

MAXIMAL SUBSEMIGROUPS OF INFINITE SYMMETRIC GROUPS

Brazil et al. [‘Maximal subgroups of infinite symmetric groups’, Proc. Lond. Math. Soc. (3)68(1) (1994), 77–111] provided a new family of maximal subgroups of the symmetric group

$G(X)$

defined on an infinite set X. It is easy to see that, in this case,

$G(X)$

contains subsemigroups that are not groups, but nothing is known about nongroup maximal subsemigroups of

$G(X)$

. We provide infinitely many examples of such semigroups.

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

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society