亚环的极大环子群的共轭类𝑝-groups

IF 0.4 3区数学 Q4 MATHEMATICS

Journal of Group Theory Pub Date : 2022-10-15 DOI:10.1515/jgth-2022-0103

M. Bianchi, R. Camina, M. Lewis

{"title":"亚环的极大环子群的共轭类𝑝-groups","authors":"M. Bianchi, R. Camina, M. Lewis","doi":"10.1515/jgth-2022-0103","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we set η ⁢ ( G ) \\eta(G) to be the number of conjugacy classes of maximal cyclic subgroups of a finite group 𝐺. We compute η ⁢ ( G ) \\eta(G) for all metacyclic 𝑝-groups. We show that if 𝐺 is a metacyclic 𝑝-group of order p n p^{n} that is not dihedral, generalized quaternion, or semi-dihedral, then η ⁢ ( G ) ≥ n - 2 \\eta(G)\\geq n-2 , and we determine when equality holds.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":"29 1","pages":"377 - 398"},"PeriodicalIF":0.4000,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Conjugacy classes of maximal cyclic subgroups of metacyclic 𝑝-groups\",\"authors\":\"M. Bianchi, R. Camina, M. Lewis\",\"doi\":\"10.1515/jgth-2022-0103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we set η ⁢ ( G ) \\\\eta(G) to be the number of conjugacy classes of maximal cyclic subgroups of a finite group 𝐺. We compute η ⁢ ( G ) \\\\eta(G) for all metacyclic 𝑝-groups. We show that if 𝐺 is a metacyclic 𝑝-group of order p n p^{n} that is not dihedral, generalized quaternion, or semi-dihedral, then η ⁢ ( G ) ≥ n - 2 \\\\eta(G)\\\\geq n-2 , and we determine when equality holds.\",\"PeriodicalId\":50188,\"journal\":{\"name\":\"Journal of Group Theory\",\"volume\":\"29 1\",\"pages\":\"377 - 398\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-10-15\",\"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-2022-0103\",\"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-2022-0103","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

摘要:本文设η (G) \eta (G)为有限群𝐺的极大循环子群的共轭类的个数。我们计算所有元环𝑝-groups的η∑(G) \eta (G)。我们证明了如果𝐺是p n p^{n}阶的元环𝑝-group，它不是二面体、广义四元数或半二面体，则η∑(G)≥n-2 \eta (G) \geq n-2，并确定了等式在什么时候成立。

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

Conjugacy classes of maximal cyclic subgroups of metacyclic 𝑝-groups

Abstract In this paper, we set η ⁢ ( G ) \eta(G) to be the number of conjugacy classes of maximal cyclic subgroups of a finite group 𝐺. We compute η ⁢ ( G ) \eta(G) for all metacyclic 𝑝-groups. We show that if 𝐺 is a metacyclic 𝑝-group of order p n p^{n} that is not dihedral, generalized quaternion, or semi-dihedral, then η ⁢ ( G ) ≥ n - 2 \eta(G)\geq n-2 , and we determine when equality holds.

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