Abstract
We prove that the natural map , where is a torsion-free group and is obtained by adding a new generator and a new relator , is surjective only if is conjugate to or where . This solves a special case of the surjectivity problem for group extensions, raised by Cohen [Topology 16 (1977) 79–88].
Citation
Marshall M Cohen. Colin Rourke. "The surjectivity problem for one-generator, one-relator extensions of torsion-free groups." Geom. Topol. 5 (1) 127 - 142, 2001. https://doi.org/10.2140/gt.2001.5.127
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