2010/06/02 by Martin W. Liebeck, E. A. O’Brien, Aner Shalev +1 · 1 citation
Mathematics · Computer Science · #Finite Group Theory Research #Coding theory and cryptography #Geometric and Algebraic Topology #Conjecture #Mathematics #Commutator #Simple (philosophy) #Character (mathematics) #Pure mathematics #Abelian group #Simple group #Group (periodic table) #Classification of finite simple groups #Algebra over a field #Finite group #Combinatorics #Group theory #Group of Lie type #Geometry
paper · pdf · doi:10.4171/jems/220
openalex publication_date 2010/06/02 · openalex created_date 2022/02/24 · openalex updated_date 2026/07/22
The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remained open for various infinite families of simple groups. In this paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.