Geodesic
On metabelian groups with derived quotient an elementary abelian $2$-group of rank~$3$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 361-375

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Necessary and sufficient conditions in terms of rank and exponent for the existence of torsion-free metabelian groups with derived quotient an elementary abelian $p$-group of rank $k$ are formulated. 
@article{SEMR_2007_4_a22,
     author = {V. V. Bludov and L. V. Dolbak},
     title = {On metabelian groups with derived quotient an elementary abelian $2$-group of rank~$3$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {361--375},
     publisher = {mathdoc},
     volume = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a22/}
}
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V. V. Bludov; L. V. Dolbak. On metabelian groups with derived quotient an elementary abelian $2$-group of rank~$3$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 361-375. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a22/