关于正子群的共轭类图

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-07-26 DOI:10.1142/s1005386722000335

Ruifang Chen, Xianhe Zhao

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引用次数: 0

摘要

设[公式:见文]是一个有限群，[公式:见文]是[公式:见文]的正规子群。用[公式:见文]表示顶点均不同的图[公式:见文]-[公式:见文]中非中心元素的共轭类大小，且[公式:见文]的两个顶点相邻当且仅当它们不是素数。我们证明，如果中心[公式:见文]和[公式:见文]是[公式:见文]的[公式:见文]-正则，那么[公式:见文]的一个部分是一个拟frobenius群，或者[公式:见文]是一个具有[公式:见文]顶点的完全图。

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On Conjugacy Class Graph of Normal Subgroup

Let [Formula: see text] be a finite group and [Formula: see text] a normal subgroup of [Formula: see text]. Denote by [Formula: see text] the graph whose vertices are all distinct [Formula: see text]-conjugacy class sizes of non-central elements in [Formula: see text], and two vertices of [Formula: see text] are adjacent if and only if they are not coprime numbers. We prove that if the center [Formula: see text] and [Formula: see text]is [Formula: see text]-regular for [Formula: see text], then either a section of [Formula: see text]is a quasi-Frobenius group or [Formula: see text] is a complete graph with [Formula: see text] vertices.

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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.