{"title":"2p阶三次对称图的二生成2群盖的注记","authors":"Xue Wang, Jin-Xin Zhou","doi":"10.1142/s1005386722000505","DOIUrl":null,"url":null,"abstract":"Let [Formula: see text] be a prime. In this paper, a complete classification of edge-transitive [Formula: see text]-covers of a cubic symmetric graph of order [Formula: see text] is given for the case when [Formula: see text] is a two-generator 2-group whose derived subgroup is either isomorphic to [Formula: see text] or generated by at most two elements. As an application, it is shown that 11 is the smallest value of [Formula: see text] for which there exist infinitely many cubic semisymmetric graphs with order of the form [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":"12 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Note on Two-Generator 2-Group Covers of Cubic Symmetric Graphs of Order 2p\",\"authors\":\"Xue Wang, Jin-Xin Zhou\",\"doi\":\"10.1142/s1005386722000505\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let [Formula: see text] be a prime. In this paper, a complete classification of edge-transitive [Formula: see text]-covers of a cubic symmetric graph of order [Formula: see text] is given for the case when [Formula: see text] is a two-generator 2-group whose derived subgroup is either isomorphic to [Formula: see text] or generated by at most two elements. As an application, it is shown that 11 is the smallest value of [Formula: see text] for which there exist infinitely many cubic semisymmetric graphs with order of the form [Formula: see text].\",\"PeriodicalId\":50958,\"journal\":{\"name\":\"Algebra Colloquium\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Colloquium\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1005386722000505\",\"RegionNum\":4,\"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":"Algebra Colloquium","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1005386722000505","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Note on Two-Generator 2-Group Covers of Cubic Symmetric Graphs of Order 2p
Let [Formula: see text] be a prime. In this paper, a complete classification of edge-transitive [Formula: see text]-covers of a cubic symmetric graph of order [Formula: see text] is given for the case when [Formula: see text] is a two-generator 2-group whose derived subgroup is either isomorphic to [Formula: see text] or generated by at most two elements. As an application, it is shown that 11 is the smallest value of [Formula: see text] for which there exist infinitely many cubic semisymmetric graphs with order of the form [Formula: see text].
期刊介绍：
Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.
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