N-group

''The term N-group is also used for a group satisfying the normalizer condition. Note that this meaning is entirely different''

History
The notion of N-group was studied extensively, and all finite N-groups were classified, in a monumental paper by John G. Thompson, titled Nonsolvable finite groups all of whose local subgroups are solvable.

Definition
A group is termed an N-group if it satisfies the following equivalent conditions:

Facts

 * Finite N-group is solvable or almost simple
 * Classification of finite N-groups