Section: New Results

Formal proof of the Feit-Thompson theorem

Participants : Laurence Rideau, Laurent Théry.

The Feit-Thompson theorem, established in the beginning of the 1960s, states that every odd-order finite group is solvable. The proof of this result was initially published in an article with around 250 pages. This proof was cleaned by a team of mathematicians and re-published in the form of two books, totaling approximately the same number of pages. But these books also rested on some general knowledge about groups and various areas of algebras.

All this knowledge is now formally described in the Mathematical Components library. The proof of the theorem has been completed in September 2012. The team that achieved this result includes members of the Marelle project-team, along with members of the Typical project-team at Inria Saclay-Ile de France, members of the Microsoft Research Cambridge laboratory, and guests from other institutions.

This year, the members of the Marelle team concentrated on the following topics:

• General character theory: chapters 5 and 6 of the book by Isaacs,

• Character theory for the odd order theorem: chapters 1 to 4 of the book of the book by Peterfalvi.

More information at http://www.msr-inria.inria.fr/Projects/math-components/feit-thompson .