Normalp-Subgroups of the Automorphism Group of an Abelianp-Group Original Research Article

We will show that for any integern ≥ 0, the automorphism group of an abelianp-groupG,p ≥ 3, contains a unique subgroup which is maximal with respect to being normal and having exponent less than or equal topn. This subgroup is Π ∩ Fix pnG, where Π is the unique maximal normalp-subgroup of Aut G, and Fix pnG = {α set membership, variant Aut GαpnG = 1}. An application of this result extends earlier results on how to find the finite Ulm invariants of a reduced abelianp-group fromp ≥ 5 to all odd primes.