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The surjectivity problem for one-generator,, one-relator extensions of torsion-free groups

Marshall M Cohen·Colin Rourke
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Abstract

We use Klyachko's methods to prove that the natural map G to G-hat, where G is a torsion-free group and G-hat is obtained by adding a new generator t and a new relator w, is surjective only if w is conjugate to gt or gt^{-1} for some g in G. This solves a special case of the surjectivity problem for group extensions, raised by Cohen [Whitehead torsion, group extensions, and Zeeman's conjecture in high dimensions, Topology, 16 (1977) 79--88].

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Marshall M Cohen, Colin Rourke. 2000-09-10. The surjectivity problem for one-generator,, one-relator extensions of torsion-free groups. https://doi.org/10.2140/gt.2001.5.127

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