Walter theorem
In mathematics, the Walter theorem, proved by, describes the finite groups whose Sylow 2-subgroup is abelian. used Bender's method to give a simpler proof.Statement
Walter's theorem states that if G is a finite group whose 2-sylow subgroups are abelian, then G/O has a normal subgroup of odd index that is a product of groups each of which is a 2-group or one of the simple groups PSL2 for q = 2n or q = 3 or 5 mod 8, or the Janko group J1, or Ree groups 2G2.
The original statement of Walter's theorem did not quite identify the Ree groups, but only stated that the corresponding groups have a similar subgroup structure as Ree groups. and later showed that they are all Ree groups, and gave a unified exposition of this result.
