Geodesic
An example of a finitely presented amenable group not belonging to the class $EG$
Sbornik. Mathematics, Tome 189 (1998) no. 1, pp. 75-95
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An example of a finitely presented amenable group not belonging to the class $EG$ of elementary amenable groups is constructed. By this means, a solution of the Day problem in the class of finitely presented groups is given. 
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R. I. Grigorchuk. An example of a finitely presented amenable group not belonging to the class $EG$. Sbornik. Mathematics, Tome 189 (1998) no. 1, pp. 75-95. http://geodesic.mathdoc.fr/item/SM_1998_189_1_a3/

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