Automorphism Groups of Finite Abelian p-groups and Transvections

摘要

We define a particular type of automorphisms called transvections on a finite finite abelian p-group H-p. It is proved that the subgroup E of the automorphism group Aut(H-p) of H-p generated by those transvections is normal in it, and that Aut(H-p) can be written as the product of E and some abelian subgroup K. The center of Aut(H-p) is also determined.