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 harv|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 harv|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 harv|Feit|Hall|Thompson|1961. The complete solution was given in harv|Feit|Thompson|1963, but further work on CN groups was done in harv|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.

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CN group

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