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Torsion-free word hyperbolic groups are noncommutatively slender

Samuel M. Corson

Mathematics Department, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA

E-mail Address: samuel.m.corson@vanderbilt.edu

https://doi.org/10.1142/S0218196716500636Cited by:4 (Source: Crossref)

Abstract

In this paper, we prove the claim given in the title. A group $G$ is noncommutatively slender if each map from the fundamental group of the Hawaiian Earring to $G$ factors through projection to a canonical free subgroup. Higman, in his seminal 1952 paper [Unrestricted free products and varieties of topological groups, J. London Math. Soc.27 (1952) 73–81], proved that free groups are noncommutatively slender. Such groups were first defined by Eda in [Free $σ$ -products and noncommutatively slender groups, J. Algebra148 (1992) 243–263]. Eda has asked which finitely presented groups are noncommutatively slender. This result demonstrates that random finitely presented groups in the few-relator sense are noncommutatively slender.

Communicated by A. Olshanskii

Keywords:

AMSC: 57M07

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