Hall's Theorem for limit groups

2006/05/19 by Henry Wilton, Wilton, Henry · 5 citations
Mathematics · #20E05) #20F65 (20E26 #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT #msc:20F65

paper · pdf · doi:10.48550/arxiv.math/0605546

39 pages, 4 figures, added a double-coset-separability result, to appear in GAFA

openalex publication_date 2006/05/19 · arxiv created 2007/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two properties. This answers a question of Sela.

Cited by

• Non-closed subgroups of weakly branch groups
• Homological torsion growth in non-normal chains of graphs of free groups
• Virtual homological torsion in graphs of free groups with cyclic edge groups
• Virtual retractions in free constructions
• Product separability in central extensions

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• Limit Groups are Subgroup Conjugacy Separable
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