3-step group

In mathematics, a 3-step group is a special sort of group of Fitting length at most 3, that is used in the classification of CN groups and in the Feit–Thompson theorem. The definition of a 3-step group in these two cases is slightly different.
CN groups.
In the theory of CN groups, a 3-step group (for some prime "p") is a group such that:
Any 3-step group is a solvable CN-group, and conversely any solvable CN-group is either nilpotent, or a Frobenius group, or a 3-step group.
Example: the symmetric group "S"4 is a 3-step group for the prime "p"=2.
Odd order groups.
 defined a three-step group to be a group "G" satisfying the following conditions: