On groups whose normal closure of 2-generated subgroups are 3-nilpotent
On groups whose normal closure of 2-generated subgroups are 3-nilpotent
(Russian, English abstract)
Siberian Electronic Mathematical Reports, 23, 1, pp. 420-430 (2026)
Abstract:
In this paper, we continue to study groups whose normal closure of each 2-generated subgroup is a nilpotent group. It is proved that there exists a non-metabelian group without elements of order 2, the normal closure of each 2-generated subgroup of which is a nilpotent group of class no more than 3.
Keywords: nilpotent group, metabelian group, normal closure of a subgroup, Levy class, variety, quasivariety.