Class two $p$ groups as fixed point free automorphism groups

Abstract

CASS TWO p eROITPS 123 (II.8) Suppose M <_ G is normal in AG. Assume r G. Then we may choose r' rM so that Ca Or') A r (AM)' A (AM)'. Let Ao A r (AM)'. Now rM e Ca/ (Ao). So we may choose r' e M so thatr' Ca(Ao) by (II.5). Then C (') A r (AM)' A n (AM)'= Ao.