Thompson uniqueness theorem

In mathematical finite group theory, Thompson's original uniqueness theorem (Feit & Thompson 1963, theorems 24.5 and 25.2) states that in a minimal simple finite group of odd order there is a unique maximal subgroup containing a given elementary abelian subgroup of rank 3. Bender (1973) gave a shorter proof of the uniqueness theorem.

References

• Bender, Helmut (1970), "On the uniqueness theorem", Illinois Journal of Mathematics, 14: 376–384, ISSN 0019-2082, MR 0262351 
• Bender, Helmut; Glauberman, George (1994), Local analysis for the odd order theorem, London Mathematical Society Lecture Note Series, 188, Cambridge University Press, ISBN 978-0-521-45716-3, MR 1311244 
• Feit, Walter; Thompson, John G. (1963), "Solvability of groups of odd order", Pacific Journal of Mathematics, 13: 775–1029, ISSN 0030-8730, MR 0166261