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4.8 (1973)

Solved

Suppose $G$ is a finitely generated free-by-cyclic group. Is $G$ finitely presented?

Contributor: G. Baumslag

Progress

Yes, it is; moreover, every finitely generated subgroup is finitely presented. For infinite cyclic extensions this is proved in (M. Feighn, M. Handel, Ann. Math., 149, no. 3 (1999), 1061–1077), while another easier argument applies for finite cyclic extensions.

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