A generalization of groups with many almost normal subgroups - Russo, F.G. (Algebra and Discrete Mathematics, 2010)
A subgroup H of a group G is called almost normal in G if it has finitely many conjugates in G. A classic result of B. H. Neumann informs us that |G:Z(G)| is finite if and only if each H is almost normal in G. Starting from this result, we investigate the structure of a group in which each non-finitely generated subgroup satisfies a property, which is weaker to be almost normal