2p阶三次对称图的二生成2群盖的注记

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

Xue Wang, Jin-Xin Zhou

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引用次数: 0

摘要

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。

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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].

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