Bounding the order of finite p^′- subgroups of \rm GL(n,ℂ)

2023/01/24 by Geoffrey Robinson, Robinson, Geoffrey
Mathematics · #20C20 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2301.10111

openalex publication_date 2023/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove: \medskip \noindent \bf Theorem A: \emph There is a fixed constant C such that for any positive integer n and prime p, every finite subgroup G of order coprime to p of \rm GL(n,ℂ) has an Abelian normal subgroup A with [G:A] ≤ (Cp)^n-1.

Related

• Group Orders That Imply a Nontrivial p-Core
• On finite groups with certain complemented p-subgroups
• Groups having all elements off a normal subgroup with prime power order
• A connection between the number of subgroups and the order of a finite group
• Bounding the order of complex linear groups and permutation groups with selected composition factors