The relative hyperbolicity of one-relator relative presentations

2008/07/16 by Le Thi Giang, Giang, Le Thi
Mathematics · #20F05 #20F10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:20F05 #msc:20F10

paper · pdf · doi:10.48550/arxiv.0807.2487

10 pages, 7 figures

arxiv created 2008/07/16 · arxiv updated 2009/12/01

Abstract

We prove that if G is a free-torsion group and w(t) is a word in the alphabet G \sqcup \t^{± 1}\ with exponent sum one, then the group <G,t|(w(t))^k = 1>, where k ≥ 2, is relatively hyperbolic with respect to G.

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