Infinite periodic groups of even exponents

2018/10/19 by Rémi Coulon, Coulon, Rémi
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1810.08372

openalex publication_date 2018/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new proof that free Burnside groups of sufficiently large even exponents are infinite. The method is very flexible and can also be used to study (partially) periodic quotients of any group which admits an action on a hyperbolic space satisfying a weak form of acylindricity.

Related

• Equations in Burnside groups
• On subgroups of free Burnside groups of large odd exponent
• The Burnside problem for odd exponents
• The Generalized Burnside Theorem
• A periodicity theorem for acylindrically hyperbolic groups