Feit-Thompson Theorem

Theorem

All finite groups of odd order are solvable.

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

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

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