A generalization of groups with many almost normal subgroups

Francesco G. Russo


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 \(|G:\mathbf{Z}(G)|\) 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.


Dietzmann classes; anti-\(\mathfrak{X}C\)-groups; groups with \(\mathfrak{X}\)-classes of conjugate subgroups; Chernikov groups

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