Finitely presented simple groups with at least exponential Dehn function

2023/05/24 by Matthew C. B. Zaremsky, Zaremsky, Matthew C. B. · 1 citation
Mathematics · #20E08 #20F65 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2305.15176

openalex publication_date 2023/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct examples of finitely presented simple groups whose Dehn functions are at least exponential. To the best of our knowledge, these are the first such examples known. Our examples arise from Röver-Nekrashevych groups, using carefully calibrated self-similar representations of Baumslag-Solitar groups.

Cited by

• Infinitely presented simple groups separated by homological finiteness properties

Related

• Polynomially-bounded Dehn functions of groups
• Super-exponential 2-dimensional Dehn functions
• Groups with quadratic-non-quadratic Dehn functions
• The Dehn function of Baumslag's Metabelian Group
• Groups with small Dehn functions and bipartite chord diagrams