Commutators cannot be proper powers in metric small-cancellation torsion-free groups
arXiv:1210.7908
Abstract
A nontrivial commutator cannot be a proper power in a torsion-free group satisfying C'(λ) small cancellation condition with sufficiently small λ.
14 pages, 13 figures. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V2: a minor correction of the proof of Lemma 3 made and an acknowledgement added. V3: minor corrections in Lemma 2 and the far-from-junction-collision lemma