G-manifolds of nilpotent groups and manifolds of power groups

The work is devoted to the theory of manifolds in the category of G-groups and in the category of power groups. Nilpotent manifolds in these categories are studied. Some new notions in group theory are introduced and studied: G-manifolds, groups of reduced G-identities, commutator subgroups, etc. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 46, Algebra, 2007.