Geodesic
Matrix representability of nilpotent products of groups
Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 383-394.

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Necessary and sufficient conditions are determined for the matrix representability over a field of zero characteristic of the second nilpotent product of arbitrary matrix groups and of an arbitrary nilpotent product of Abelian matrix groups. 
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     author = {Yu. E. Vapn\`e},
     title = {Matrix representability of nilpotent products of groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {383--394},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a8/}
}
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Yu. E. Vapnè. Matrix representability of nilpotent products of groups. Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 383-394. http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a8/