# Feit-Thompson Theorem

## Theorem

All finite groups of odd order are solvable.

That is, every non-abelian finite simple group is of even order.

## Source of Name

This entry was named for Walter Feit and John Griggs Thompson.

## Historical Note

The Feit-Thompson Theorem originated as a conjecture of William Burnside in the $1911$ edition of his Theory of Groups of Finite Order, 2nd ed..

He had previously raised the question in the first ($1897$) edition of that work about the existence or not of a non-abelian simple group of odd order without actually predicting the outcome.

The question was settled by Walter Feit and John Griggs Thompson in their $1963$ paper in Pacific Journal of Mathematics.