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We prove that if G is a periodic group with all subgroups subnormal, and if for every x, y \in G, G is an FC-group, then G is nilpotent.
A Generalization of a Result on Torsion-Free Groups With all Subgroups Subnormal
Torsion-Free Groups Subgroups Subnormal
2010/2/26
The main result in this paper is the following: Let G be a torsion-free locally nilpotent group and let F be a finitely generated subgroup of G. If every subgroup of G containing F is subnormal in G, ...