Geodesic
On the cardinality of relator sets of groups $F/\prod [N_i,N_j]$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 129-136

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The present paper generalizes the results of our paper "On the finite presentability of the group $F/[M,N]$" to an arbitrary family of normal subgroups $\{N_i \mid i\in I\}$ in a free group $F$. We obtain conditions for finite presentability of the quotient group $F/\prod [N_i,N_j]$. In both papers, the proof of the main result is based on the properties of verbal wreath products introduced by Alfred Lvovich Shmel'kin. 
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     author = {O. V. Kulikova and A. Yu. Olshanskii},
     title = {On the cardinality of relator sets of groups $F/\prod [N_i,N_j]$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {129--136},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a8/}
}
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O. V. Kulikova; A. Yu. Olshanskii. On the cardinality of relator sets of groups $F/\prod [N_i,N_j]$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 129-136. http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a8/