Commuting involutions in finite simple groups: Commuting involutions in finite simple groups

We prove that if G is a finite simple group and x , y ∈ G are involutions, then | x G ∩ C G ( y ) | → ∞ as | G | → ∞ . This extends results of Guralnick–Robinson and Skresanov. We also prove a related result about C G ( t ) / O ( C G ( t ) ) that does not require the classification of finite simple...

Full description

Saved in:
Bibliographic Details
Published in:European journal of mathematics 2025, Vol.11 (1)
Main Authors: Guralnick, Robert, Robinson, Geoffrey R.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Mathematics
Mathematics and Statistics
Research Article
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that if G is a finite simple group and x , y ∈ G are involutions, then | x G ∩ C G ( y ) | → ∞ as | G | → ∞ . This extends results of Guralnick–Robinson and Skresanov. We also prove a related result about C G ( t ) / O ( C G ( t ) ) that does not require the classification of finite simple groups.
ISSN:2199-675X
2199-6768
DOI:10.1007/s40879-024-00793-7