Nilpotent injectors in minimal simple groups

An odd nilpotent injector of a finite group G is defined to be a subgroup which is maximal subject to being nilpotent of odd order and containing a subgroup of maximal order amongst all abelian subgroups of odd order. We prove that the odd nilpotent injectors of a minimal simple group are all conjugate, extending the result from soluble groups. The proof does not use the classification of minimal simple groups.