Let r be the automorphism group of a nonelementary reduced abelian p-group, p > 5. It is shown that every noncentral norinal subgroup of r contains a noncentral elementary abelian normal p-subgroup of r of rank at least 2. 1. The result. Throughout the following, G is a reduced p-primary abelian group, p > 5, and F is the group of all automorphisms of G. If G is elementary abelian then the normal structure of F is well known. In particular, F does not contain normal p-subgroups #' 1 [2, pp. 41, 451. If pG #' 0 then F does possess nontrivial normal p-subgroups. Moreover, in this case, every noncentral (i.e. not contained in the center ZF of F) normal subgroup of F contains a noncentral normal p-subgroup N of F such that NW = 1 [6, Theorem Al. The purpose of this note is to prove the following result which is considerably stronger. Theorem. Let F be the automorphism group of a nonelementary reduced abelian p-group, p > 5. Then every noncentral normal subgroup of F contains a noncentral elementary abelian normal p-subgroup of F of rank at least 2. The hypothesis p #' 2 is indispensable since the dihedral group D4 occurs as an automorphism group of an abelian 2-group (namely G = Z(2) ED Z(4); D4 contains a [noncentrall cyclic normal subgroup of order 4 whose socle is the center of D4). Whether the above Theorem holds true for p = 3 is an open question. 2. Tools. Notation and terminology will be that of [31 and [61 unless., explained otherwise. Calculations involving automorphisms are carried out in the endomorphism ring of G. The following facts are used frequently. Note that mappings are written to the right. Received by the editors December 26, 1973. AMS (MOS) subject classifications (1970). Primary 20K30, 20K10, 2OF 15; Secondary 2OF30Q