Finite CN-group

Definition
A finite CN-group is a finite group that is also a CN-group.

Basic facts

 * Sylow subgroups for distinct primes in CN-group centralize each other iff they have non-identity elements that centralize each other
 * Commuting of non-identity elements defines an equivalence relation between prime divisors of the order of a finite CN-group

More advanced facts

 * 3-step group implies solvable CN-group
 * Classification of finite solvable CN-groups