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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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/

[1] Kulikova O. V., Olshanskii A. Yu., “O konechnoi opredelennosti gruppy $F/[M,N]$”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2006, no. 6, 19–21 | MR | Zbl

[2] Magnus V., Karras A., Soliter D., Kombinatornaya teoriya grupp, Nauka, M., 1974

[3] Neiman Kh., Mnogoobraziya grupp, Mir, M., 1969

[4] Shmelkin A. L., “Spleteniya i mnogoobraziya grupp”, Izv. AN SSSR. Ser. matem., 29:1 (1965), 149–170 | Zbl

[5] Abarbanel J., Rosset S., “The Schur multiplier of $F/[R,S]$”, J. Pure Appl. Algebra, 198 (2005), 1–8 | MR | Zbl

[6] Baumslag G., Strebel R., Thomson W., “On the multiplicator of $F/\gamma_cR$”, J. Pure Appl. Algebra, 16 (1980), 121–132 | MR | Zbl