On the structure of subgroups of a nilpotent nonperiodic group

Abstract

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, andϕ is a structural isomorphism of the group G, then N(H) ϕ = N(H ϕ ).