Abstract
We prove that if G is a torsion-free group and w is a word in the alphabet G ⊔ {t±1} with exponent sum 1 in t, then the group 〈 G, t | wk = 1〉, for k ⩾ 2, is relatively hyperbolic with respect to G.
Received: 2008-07-18
Revised: 2008-11-29
Published Online: 2009-06-22
Published in Print: 2009-November
© de Gruyter 2009