Indecomposable explicit abelian group

(withdrawn.) For every lambda we give an explicit construction of an Abelian group with no non-trivial automorphisms. In particular the group absolutely has no non-trivial automorphisms, hence is absolutely indecomposable. Earlier we knew a stronger existence theorem but only up to a quite large cardinal which was a necessary restriction. In another direction the construction does not use the axiom of choice.