**MSC:**- 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks, See also {20F17}
- 20D20 Sylow subgroups, Sylow properties, $pi$-groups,

as as subclass of CN-groups in which the centralizers of all nontrivial

Elements are nilpotent. Then we give in generalization of a Theorem of

Deaconescu necessary and sufficient conditions to be such group.