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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     author = {R. I. Grigorchuk},
     title = {An example of a~finitely presented amenable  group not belonging to the~class~$EG$},
     journal = {Sbornik. Mathematics},
     pages = {75--95},
     publisher = {mathdoc},
     volume = {189},
     number = {1},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_1_a3/}
}
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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/