Indecomposable explicit abelian group

TL;DR

This paper presents an explicit construction of abelian groups that are absolutely indecomposable with no non-trivial automorphisms, avoiding the axiom of choice and improving on previous existence results.

Contribution

It provides a new explicit method to construct absolutely indecomposable abelian groups without relying on the axiom of choice.

Findings

Constructed abelian groups with no non-trivial automorphisms

Groups are absolutely indecomposable

Construction does not use the axiom of choice

Abstract

(withdrawn.)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.