# Feit-Thompson Theorem

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## Theorem

All finite groups of odd order are solvable.

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

## Proof

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## 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*.

## Sources

- 1963: John Griggs Thompson and Walter Feit:
*Solvability of groups of odd order*(*Pacific J. Math.***Vol. 13**: pp. 775 – 1029)

- 1978: John S. Rose:
*A Course on Group Theory*... (previous) ... (next): $1$: Introduction to Finite Group Theory: $1.12$ - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Feit-Thompson theorem**