# CN-group

In mathematics, in the area of algebra known as group theory, a more than fifty-year effort was made to answer a conjecture of (Burnside 1911): are all groups of odd order solvable? Progress was made by showing that CA-groups, groups in which the centralizer of a non-identity element is abelian, of odd order are solvable (Suzuki 1957). Further progress was made showing that **CN-groups**, groups in which the centralizer of a non-identity element is nilpotent, of odd order are solvable (Feit, Hall & Thompson 1961). The complete solution was given in (Feit & Thompson 1963), but further work on CN-groups was done in (Suzuki 1961), giving more detailed information about the structure of these groups. For instance, a non-solvable CN-group *G* is such that its largest solvable normal subgroup *O*_{∞}(*G*) is a 2-group, and the quotient is a group of even order.