FC-groups with Few Subnormal Non-normal Subgroups

A group G is said to be an FC -group if every conjugacy class of G has finite order and is said to be a T -group if every subnormal subgroup is normal in G . In this paper we give a characterization of groups that are both FC -groups and T -groups and go further in the study of FC -groups with few subnormal non-normal subgroups in the sense of the chain conditions. The structure of FC -groups satisfying the maximal, the minimal and the double chain condition on subnormal non-normal subgroups will be described.