CN-group

Origin
The concept and terminology of CN-groups was introduced by Michio Suzuki in his attempts to solve Burnside's conjecture (which later became the odd-order theorem).

Definition
Below are listed some equivalent definitions of CN-group, also called centralizer is nilpotent group:

Facts

 * For finite CN-groups: Sylow subgroups for distinct primes in CN-group centralize each other iff they have non-identity elements that centralize each other
 * Quotient group of finite CN-group by solvable normal subgroup is CN-group