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Chong–Wise conjecture on embedding free-by-cyclic groups

Show that every finitely generated free-by-cyclic group embeds into a free-by-cyclic group with finitely generated free kernel.

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Background

Embedding general free-by-cyclic groups into those with finitely generated free kernels would propagate many geometric and profinite properties to broader classes, including residual finiteness via linearity arguments.

References

\begin{conjecture}[Chong--Wise] If $G$ is a finitely generated free-by-cyclic group, then $G$ is a subgroup of a {finitely generated free}-by-cyclic group. \end{conjecture}

— The theory of one-relator groups: history and recent progress (2501.18306 - Linton et al., 30 Jan 2025) in Subsection 5.6 (Free-by-cyclic one-relator groups)