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16.52 (2006)

Solved

Is every finitely presented elementary amenable group solvable-by-finite?

Contributor: P. Linnell, T. Schick

Progress

No, not every. I. Belegradek and Y. Cornulier have pointed out that the groups in (C. H. Houghton, Arch. Math. (Basel), 31, no. 3 (1978/79), 254–258) are finitely presented as shown in (K. S. Brown, J. Pure Appl. Algebra, 44, no. 1–3 (1987), 45–75) and elementary amenable, but not virtually solvable; http://mathoverflow.net/questions/107996.

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