On finite groups of odd order admitting involutory automorphisms (Q923722)

Let G be a finite group of odd order and \(\tau\) an involutory automorphism of G. The set of all elements of G which are left fixed by \(\tau\) is denoted by H. Some group theorists who have been interested in the structure of G in case that H is nilpotent studied G making use of the celebrated theorem on the solvability of groups of odd order by W. Feit and J. G. Thompson. In his paper, the author provides a direct proof of the following result: Let G and \(\tau\) be as above with H nilpotent. Then G is solvable.