On the structure of subgroups of a nilpotent nonperiodic group

The structural characteristic of the normal divisor in a locally nilpotent torsion-free group is given. Moreover, a property of structural isomorphisms of locally nilpotent groups containing no less than two independent elements of infinite order is proved: if $H$ is the subgroup of the mentioned group $G$, $N(H)$ is its normalizer in $G$, and $\varphi$ is a structural isomorphism of the group $G$, then $N(H)^\varphi=N(H^\varphi)$.