Geodesic
Groups with restrictions on normal subgroups
Algebra i logika, Tome 63 (2024) no. 1, pp. 3-14

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that if $G$ is a group without elements of order $2$, and the normal closure of every $2$-generated subgroup of $G$ is a nilpotent group of class at most $3$, then $G$ will be a nilpotent group of class at most $4$. It is also shown that the restriction on second-order elements cannot be lifted.
Keywords: nilpotent group, normal closure of subgroup, Levi class, variety, quasivariety. 
@article{AL_2024_63_1_a0,
     author = {A. I. Budkin},
     title = {Groups with restrictions on normal subgroups},
     journal = {Algebra i logika},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2024_63_1_a0/}
}
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A. I. Budkin. Groups with restrictions on normal subgroups. Algebra i logika, Tome 63 (2024) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/AL_2024_63_1_a0/