Groups with restrictions on normal subgroups

A. I. Budkin

Algebra i logika, Tome 63 (2024) no. 1, pp. 3-14

Résumé

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.

Détail

Keywords: nilpotent group, normal closure of subgroup, Levi class, variety, quasivariety.

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