广义四元组上双凯利图的同构性

arXiv - MATH - Combinatorics Pub Date : 2024-09-18 DOI:arxiv-2409.11918

Jin-Hua Xie

{"title":"广义四元组上双凯利图的同构性","authors":"Jin-Hua Xie","doi":"arxiv-2409.11918","DOIUrl":null,"url":null,"abstract":"Let $m$ be a positive integer. A group $G$ is said to be an $m$-BCI-group if\n$G$ has the $k$-BCI property for all positive integers $k$ at most $m$. Let $G$\nbe a generalized quaternion group of order $4n$ with $n\\geq 2$. It is shown\nthat $G$ is a 3-BCI-group if and only if $G$ is a $2$-BCI-group if and only if\n$n=2$ or $n$ is odd.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Isomorphisms of bi-Cayley graphs on generalized quaternion groups\",\"authors\":\"Jin-Hua Xie\",\"doi\":\"arxiv-2409.11918\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $m$ be a positive integer. A group $G$ is said to be an $m$-BCI-group if\\n$G$ has the $k$-BCI property for all positive integers $k$ at most $m$. Let $G$\\nbe a generalized quaternion group of order $4n$ with $n\\\\geq 2$. It is shown\\nthat $G$ is a 3-BCI-group if and only if $G$ is a $2$-BCI-group if and only if\\n$n=2$ or $n$ is odd.\",\"PeriodicalId\":501407,\"journal\":{\"name\":\"arXiv - MATH - Combinatorics\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11918\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11918","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

设 $m$ 为正整数。如果$G$对所有最多为$m$的正整数$k$具有$k$-BCI性质，则称$G$为$m$-BCI群。让 $G$ 是一个阶数为 $4n$ 的广义四元数群，其阶数为 $n\geq 2$。当且仅当 $n=2$ 或 $n$ 为奇数时，当且仅当 $G$ 为 2$-BCI 群时，$G$ 是一个 3-BCI 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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Isomorphisms of bi-Cayley graphs on generalized quaternion groups

Let $m$ be a positive integer. A group $G$ is said to be an $m$-BCI-group if $G$ has the $k$-BCI property for all positive integers $k$ at most $m$. Let $G$ be a generalized quaternion group of order $4n$ with $n\geq 2$. It is shown that $G$ is a 3-BCI-group if and only if $G$ is a $2$-BCI-group if and only if $n=2$ or $n$ is odd.

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

arXiv - MATH - Combinatorics

自引率

0.00%

发文量

期刊最新文献

A note on connectivity in directed graphs Proof of a conjecture on graph polytope Generalized Andrásfai--Erdős--Sós theorems for odd cycles The repetition threshold for ternary rich words Isomorphisms of bi-Cayley graphs on generalized quaternion groups