Normalizer condition implies locally nilpotent

This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., group satisfying normalizer condition) must also satisfy the second group property (i.e., locally nilpotent group)
View all group property implications | View all group property non-implications
Get more facts about group satisfying normalizer condition|Get more facts about locally nilpotent group

Statement

Suppose $G$ is a group satisfying normalizer condition: for any proper subgroup $H$ of $G$, the normalizer $N_G(H)$ is strictly bigger than $H$. Then, $G$ is a locally nilpotent group: any finitely generated subgroup of $G$ is nilpotent.