On Groups of Odd Order Admitting an Elementary 2-Group of Automorphisms

Abstract

-Let G be a finite group of odd order with derived length k. We show that if G is acted on by an elementary abelian group A of order 2 n and C G (A) has exponent e, then G has a normal series G G 0 ! T 0 ! G 1 ! T 1 ! Á Á Á ! G n ! T n 1 such that the quotients G i =T i have fk; e; ng-bounded exponent and the quotients T i =G i1 are nilpotent of fk; e; ng-bounded class.Dedicated to Professor Said Sidki on the occasion of his 70th birthday