Rigid abelian groups and the probabilistic method
Abstract
The construction of torsion-free abelian groups with prescribed endomorphism rings starting with Corner's seminal work is a well-studied subject in the theory of abelian groups. Usually these construction work by adding elements from a (topological) completion in order to get rid of (kill) unwanted homomorphisms. The critical part is to actually prove that every unwanted homomorphism can be killed by adding a suitable element. We will demonstrate that some of those constructions can be significantly simplified by choosing the elements at random. As a result, the endomorphism ring will be almost surely prescribed, i.e., with probability one.
Cite
@article{arxiv.1107.2325,
title = {Rigid abelian groups and the probabilistic method},
author = {Gábor Braun and Sebastian Pokutta},
journal= {arXiv preprint arXiv:1107.2325},
year = {2012}
}
Comments
12 pages, submitted to the special volume of Contemporary Mathematics for the proceedings of the conference Group and Model Theory, 2011