Groups whose cyclic subnormal subgroups are normal (Q2749011)

A group is called a \(T_c\)-group if every cyclic subnormal subgroup is normal. This is a generalization of the concept of a \(T\)-group, i.e. a group in which every subnormal subgroup is normal. Using elementary arguments the author shows that soluble \(T\)-groups are metabelian and locally supersoluble. An example of a \(T_c\)-group which is not a \(T\)-group is the infinite dihedral group.NEWLINENEWLINENEWLINEThe reviewer comments that the wreath product \(A_5\text{ wr }\mathbb{Z}_2\) is a finite \(T_c\)-group which is not a \(T\)-group. Also there are finite soluble \(T_c\)-groups which are not \(T\)-groups.