A Note on Two-Generator 2-Group Covers of Cubic Symmetric Graphs of Order 2p

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-12-01 DOI:10.1142/s1005386722000505

Xue Wang, Jin-Xin Zhou

引用次数: 0

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].

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2p阶三次对称图的二生成2群盖的注记

设[公式:见文本]为素数。当[公式:见文]是两个生成子群，其派生子群与[公式:见文]同构或由至多两个元素生成时，给出了阶[公式:见文]三次对称图的边传递[盖]的完全分类。作为一个应用，证明了11是[公式:见文]的最小值，对于它，存在无穷多个阶为[公式:见文]的三次半对称图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

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.