# Thompson uniqueness theorem

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Thompson_uniqueness_theorem
> Markdown URL: https://mediated.wiki/source/Thompson_uniqueness_theorem.md
> Source: https://en.wikipedia.org/wiki/Thompson_uniqueness_theorem
> Source revision: 1136415322
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

In mathematical [finite group](/source/Finite_group) theory, Thompson's original **uniqueness theorem** (Feit & Thompson 1963, theorems 24.5 and 25.2) states that in a minimal [simple](/source/Simple_group) finite [group](/source/Group_(mathematics)) of odd [order](/source/Order_(group_theory)) there is a unique maximal [subgroup](/source/Subgroup) containing a given [elementary abelian subgroup](/source/Elementary_abelian_group) of [rank](/source/Rank_of_a_group) 3. Bender (1970) gave a shorter proof of the uniqueness theorem.

## References

- Bender, Helmut (1970), ["On the uniqueness theorem"](http://projecteuclid.org/euclid.ijm/1256053074), *Illinois Journal of Mathematics*. **14** (3): 376–384, [doi:10.1215/ijm/1256053074](https://doi.org/10.1215/ijm/1256053074). [ISSN 0019-2082](https://www.worldcat.org/issn/0019-2082). MR 0262351
- Bender, Helmut & Glauberman, George (1994), *Local analysis for the odd order theorem*, Vol. 188, London Mathematical Society Lecture Note Series, [Cambridge University Press](/source/Cambridge_University_Press), ISBN 978-0-521-45716-3. MR 1311244
- Feit, Walter & Thompson, John G. (1963), ["Solvability of groups of odd order"](http://projecteuclid.org/Dienst/UI/1.0/Journal?authority=euclid.pjm&issue=1103053941), *Pacific Journal of Mathematics*. **13**: 775–1029, [doi:10.2140/pjm.1963.13.775](https://doi.org/10.2140/pjm.1963.13.775). [ISSN 0030-8730](https://www.worldcat.org/issn/0030-8730). MR 0166261

---
Adapted from the Wikipedia article [Thompson uniqueness theorem](https://en.wikipedia.org/wiki/Thompson_uniqueness_theorem) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Thompson_uniqueness_theorem?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.