The Lengths of Certain Real Conjugacy Classes and the Related Prime Graph

The Lengths of Certain Real Conjugacy Classes and the Related Prime Graph

Let <i>G</i> be a finite group. In this paper, we study how certain arithmetical conditions on the conjugacy class lengths of real elements of <i>G</i> influence the structure of <i>G</i>. In particular, a new type of prime graph is introduced and studied. We obta...

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Bibliographic Details
Main Authors: Siqiang Yang, Xianhua Li
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Mathematics
Subjects:
real elements
primary elements
conjugacy class lengths
prime graph
<b>P</b>-groups
Online Access:https://www.mdpi.com/2227-7390/9/17/2060
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spelling doaj-46202082fc2a406395878ace72e533052021-09-09T13:52:13ZengMDPI AGMathematics2227-73902021-08-0192060206010.3390/math9172060The Lengths of Certain Real Conjugacy Classes and the Related Prime GraphSiqiang Yang0Xianhua Li1School of Mathematical Science, Guizhou Normal University, Huaxi District, GuiYang 550000, ChinaSchool of Mathematical Science, Guizhou Normal University, Huaxi District, GuiYang 550000, ChinaLet <i>G</i> be a finite group. In this paper, we study how certain arithmetical conditions on the conjugacy class lengths of real elements of <i>G</i> influence the structure of <i>G</i>. In particular, a new type of prime graph is introduced and studied. We obtain a series of theorems which generalize some existed results.https://www.mdpi.com/2227-7390/9/17/2060real elementsprimary elementsconjugacy class lengthsprime graph<b>P</b>-groups
collection DOAJ
language English
format Article
sources DOAJ
author Siqiang Yang
Xianhua Li
spellingShingle Siqiang Yang
Xianhua Li
The Lengths of Certain Real Conjugacy Classes and the Related Prime Graph
Mathematics
real elements
primary elements
conjugacy class lengths
prime graph
<b>P</b>-groups
author_facet Siqiang Yang
Xianhua Li
author_sort Siqiang Yang
title The Lengths of Certain Real Conjugacy Classes and the Related Prime Graph
title_short The Lengths of Certain Real Conjugacy Classes and the Related Prime Graph
title_full The Lengths of Certain Real Conjugacy Classes and the Related Prime Graph
title_fullStr The Lengths of Certain Real Conjugacy Classes and the Related Prime Graph
title_full_unstemmed The Lengths of Certain Real Conjugacy Classes and the Related Prime Graph
title_sort lengths of certain real conjugacy classes and the related prime graph
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-08-01
description Let <i>G</i> be a finite group. In this paper, we study how certain arithmetical conditions on the conjugacy class lengths of real elements of <i>G</i> influence the structure of <i>G</i>. In particular, a new type of prime graph is introduced and studied. We obtain a series of theorems which generalize some existed results.
topic real elements
primary elements
conjugacy class lengths
prime graph
<b>P</b>-groups
url https://www.mdpi.com/2227-7390/9/17/2060
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