On the Common Divisor Graph of the Product of Integer Multisets

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-05-06 DOI:10.1007/s41980-024-00881-0

Antonio Beltrán, Mohammad Ali Hosseinzadeh, Samaneh Hossein-Zadeh, Ali Iranmanesh

引用次数: 0

Abstract

The common divisor graph, \(\Gamma (X)\), is a graph that has been defined on a set of positive integers X. Some properties of this graph have been studied in the cases when either X is the set of character degrees or the set of conjugacy class sizes of a group. This paper deals with several properties of a particular case of the common divisor graph, \(\Gamma (Z)\), when Z is a multiset of positive integers that admits a decomposition \(Z=XY\), where \(XY=\{ xy | x\in X, y\in Y \}\) and \(1\in X\) and \(1 \in Y\). Our results can be applied for the graphs associated to character degrees and conjugacy classes of the direct product of two finite groups.

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论整数多集之积的公分子图

公因子图（\(\Gamma (X)\)）是一个定义在正整数集合 X 上的图。当 X 是一个群的特征度集合或共轭类大小集合时，该图的一些性质已被研究。本文讨论了当 Z 是一个正整数的多集时，公因子图 \(\Gamma (Z)\)的一个特殊情况的几个性质，这个多集允许分解 \(Z=XY\)，其中 \(XY=\{ xy| x\in X, y\in Y \}\)和 \(1\in X\) and\(1 \in Y\).我们的结果可以应用于与两个有限群的直积的特征度和共轭类相关的图。

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

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.