Groups with restrictions on infinite subnormal subgroups (Q1373432)

\textit{C. Casolo} [Rend. Semin. Mat. Univ. Padova 81, 107-149 (1989; Zbl 0692.20028)] studied groups in which all subnormal subgroups are almost normal, and groups in which every subnormal subgroup has finite index in its normal closure. In the article under review the authors prove that the class of groups in which all infinite subnormal subgroups are almost normal, and the class of groups in which every infinite subnormal subgroup has finite index in its normal closure coincide with the corresponding classes of groups considered by C. Casolo, so that the imposition of the mentioned properties only on the system of infinite subnormal subgroups forces all subnormal subgroups to have these properties.