On Conjugacy Class Graph of Normal Subgroup
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Published:2022-07-26
Issue:03
Volume:29
Page:437-442
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ISSN:1005-3867
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Container-title:Algebra Colloquium
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language:en
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Short-container-title:Algebra Colloq.
Author:
Chen Ruifang1,
Zhao Xianhe1
Affiliation:
1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, China
Abstract
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.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory