可解𝐴群的换向图

IF 0.4 3区数学 Q4 MATHEMATICS

Journal of Group Theory Pub Date : 2024-08-26 DOI:10.1515/jgth-2023-0076

Rachel Carleton, Mark L. Lewis

{"title":"可解𝐴群的换向图","authors":"Rachel Carleton, Mark L. Lewis","doi":"10.1515/jgth-2023-0076","DOIUrl":null,"url":null,"abstract":"Let 𝐺 be a finite group. Recall that an 𝐴-group is a group whose Sylow subgroups are all abelian. In this paper, we investigate the upper bound on the diameter of the commuting graph of a solvable 𝐴-group. Assuming that the commuting graph is connected, we show when the derived length of 𝐺 is 2, the diameter of the commuting graph will be at most 4. In the general case, we show that the diameter of the commuting graph will be at most 6. In both cases, examples are provided to show that the upper bound of the commuting graph cannot be improved.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The commuting graph of a solvable 𝐴-group\",\"authors\":\"Rachel Carleton, Mark L. Lewis\",\"doi\":\"10.1515/jgth-2023-0076\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let 𝐺 be a finite group. Recall that an 𝐴-group is a group whose Sylow subgroups are all abelian. In this paper, we investigate the upper bound on the diameter of the commuting graph of a solvable 𝐴-group. Assuming that the commuting graph is connected, we show when the derived length of 𝐺 is 2, the diameter of the commuting graph will be at most 4. In the general case, we show that the diameter of the commuting graph will be at most 6. In both cases, examples are provided to show that the upper bound of the commuting graph cannot be improved.\",\"PeriodicalId\":50188,\"journal\":{\"name\":\"Journal of Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Group Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/jgth-2023-0076\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Group Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2023-0076","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设𝐺是一个有限群。回顾一下，𝐴-群是指其 Sylow 子群都是非良群的群。本文将研究可解𝐴群换向图的直径上限。假设换向图是连通的，我们证明了当𝐺 的派生长度为 2 时，换向图的直径最多为 4；在一般情况下，我们证明了换向图的直径最多为 6。

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

The commuting graph of a solvable 𝐴-group

Let 𝐺 be a finite group. Recall that an 𝐴-group is a group whose Sylow subgroups are all abelian. In this paper, we investigate the upper bound on the diameter of the commuting graph of a solvable 𝐴-group. Assuming that the commuting graph is connected, we show when the derived length of 𝐺 is 2, the diameter of the commuting graph will be at most 4. In the general case, we show that the diameter of the commuting graph will be at most 6. In both cases, examples are provided to show that the upper bound of the commuting graph cannot be improved.

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

Journal of Group Theory 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered. Topics: Group Theory- Representation Theory of Groups- Computational Aspects of Group Theory- Combinatorics and Graph Theory- Algebra and Number Theory