Elementary equivalence of the automorphism groups of reduced Abelian   p-groups
  Consider unbounded reduced Abelian p-groups (p > 2) A and A'. In this paper, we prove that if the automorphism groups Aut A and Aut A' are elementary equivalent then the groups A and A' are equivalent in the second order logic bounded by the final rank of the basic subgroups of A and A'. 
Michael Roizner
math.GR math.LO