Geodesic
An example of a finitely defined solvable group without the maximality condition for normal subgroups
Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 287-293 
V. N. Remeslennikov. An example of a finitely defined solvable group without the maximality condition for normal subgroups. Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 287-293. http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a9/
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     author = {V. N. Remeslennikov},
     title = {An example of a finitely defined solvable group without the maximality condition for normal subgroups},
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     pages = {287--293},
     year = {1972},
     volume = {12},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

There is a finitely defined solvable group which does not satisfy the maximality condition for normal subgroups. This theorem gives a negative answer to one of the questions raised by P. Hall.