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10.37 (1986)

Solved

Suppose that $G$ is a finitely generated metabelian group all of whose integral homology groups are finitely generated. Is it true that $G$ is a group of finite rank? The answer is affirmative if $G$ splits over the derived subgroup (J. R. J. Groves, Quart. J. Math., 33, no. 132 (1982), 405–420).

Contributor: G. A. Noskov

Progress

Yes, it is (D. H. Kochloukova, Groups St. Andrews 2001 in Oxford, Vol. II, Cambridge Univ. Press, 2003, 332–343).

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