Root extraction in one-relator groups and slenderness

In this note we strengthen a result of Newman and use it to prove a conjecture of Nakamura stated in 10 Nakamura, J. (2015). Atomic properties of the Hawaiian earring group for HNN extensions. Commun. Algebra 43:4138–4147.Taylor &; Francis Online], Web of Science ®] , Google Scholar]] that torsion-free one-relator groups are noncommutatively slender.