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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{MZM_1972_12_3_a9,
     author = {V. N. Remeslennikov},
     title = {An example of a finitely defined solvable group without the maximality condition for normal subgroups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {287--293},
     year = {1972},
     volume = {12},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a9/}
}
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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/