关于有限群的权值

Q3 Mathematics

Quasigroups and Related Systems Pub Date : 2023-04-01 DOI:10.56415/qrs.v30.25

Mohammad Amin Morshedlo, M. M. Nasrabadi

{"title":"关于有限群的权值","authors":"Mohammad Amin Morshedlo, M. M. Nasrabadi","doi":"10.56415/qrs.v30.25","DOIUrl":null,"url":null,"abstract":"For a finite group G, let W(G) denotes the set of the orders of the elements of G. In this paper we study jW(G)j and show that the cyclic group of order n has the maximum value of jW(G)j among all groups of the same order. Furthermore we study this notion in nilpotent and non-nilpotent groups and state some inequality for it. Among the result we show that the minimum value of jW(G)j is power of 2 or it pertains to a non-nilpotent group.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the weight of finite groups\",\"authors\":\"Mohammad Amin Morshedlo, M. M. Nasrabadi\",\"doi\":\"10.56415/qrs.v30.25\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a finite group G, let W(G) denotes the set of the orders of the elements of G. In this paper we study jW(G)j and show that the cyclic group of order n has the maximum value of jW(G)j among all groups of the same order. Furthermore we study this notion in nilpotent and non-nilpotent groups and state some inequality for it. Among the result we show that the minimum value of jW(G)j is power of 2 or it pertains to a non-nilpotent group.\",\"PeriodicalId\":38681,\"journal\":{\"name\":\"Quasigroups and Related Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quasigroups and Related Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56415/qrs.v30.25\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v30.25","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

对于有限群G，令W(G)表示G的元素阶的集合。本文研究了jW(G)j，证明了n阶循环群在所有同阶群中具有最大的jW(G)j。进一步在幂零群和非幂零群中研究了这一概念，并给出了它的一些不等式。在这些结果中，我们证明了jW(G)j的最小值是2的幂或它属于一个非幂零群。

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

On the weight of finite groups

For a finite group G, let W(G) denotes the set of the orders of the elements of G. In this paper we study jW(G)j and show that the cyclic group of order n has the maximum value of jW(G)j among all groups of the same order. Furthermore we study this notion in nilpotent and non-nilpotent groups and state some inequality for it. Among the result we show that the minimum value of jW(G)j is power of 2 or it pertains to a non-nilpotent group.

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

Quasigroups and Related Systems Mathematics-Discrete Mathematics and Combinatorics

CiteScore

0.70

自引率

0.00%

发文量