作用于三集笛卡尔积的对称群的直积的秩、次度和亚轨道图

IF 0.2 Q4 MATHEMATICS Italian Journal of Pure and Applied Mathematics Pub Date : 2017-01-24 DOI:10.11648/J.PAMJ.20170601.11

Gikunju David Muriuki, Nyaga Lewis Namu, Rimberia Jane Kagwiria

{"title":"作用于三集笛卡尔积的对称群的直积的秩、次度和亚轨道图","authors":"Gikunju David Muriuki, Nyaga Lewis Namu, Rimberia Jane Kagwiria","doi":"10.11648/J.PAMJ.20170601.11","DOIUrl":null,"url":null,"abstract":"Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ≥ 2. In addition, we establish that the rank associated with the action is a constant 23 Further; we calculate the subdegrees associated with the action and arrange them according to their increasing magnitude.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"9 1","pages":"1"},"PeriodicalIF":0.2000,"publicationDate":"2017-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Ranks, Subdegrees and Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets\",\"authors\":\"Gikunju David Muriuki, Nyaga Lewis Namu, Rimberia Jane Kagwiria\",\"doi\":\"10.11648/J.PAMJ.20170601.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ≥ 2. In addition, we establish that the rank associated with the action is a constant 23 Further; we calculate the subdegrees associated with the action and arrange them according to their increasing magnitude.\",\"PeriodicalId\":46057,\"journal\":{\"name\":\"Italian Journal of Pure and Applied Mathematics\",\"volume\":\"9 1\",\"pages\":\"1\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2017-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Italian Journal of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11648/J.PAMJ.20170601.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Italian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11648/J.PAMJ.20170601.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

本文研究了对称群的直积作用于三集笛卡尔积的传递性和原性。我们证明了对于所有n≥2，这个作用既是传递的又是非原的。此外，我们建立了与动作相关的秩是一个常数23。我们计算与动作相关的子度，并根据它们的递增幅度排列它们。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Ranks, Subdegrees and Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets

Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ≥ 2. In addition, we establish that the rank associated with the action is a constant 23 Further; we calculate the subdegrees associated with the action and arrange them according to their increasing magnitude.

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

Italian Journal of Pure and Applied Mathematics MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The “Italian Journal of Pure and Applied Mathematics” publishes original research works containing significant results in the field of pure and applied mathematics.

from a Computational Viewpoint