What does the automorphism group of a free abelian group A know about A?

Vladimir Tolstykh

What does the automorphism group of a free abelian group A know about A?

Logic 2007-05-23 v1 Group Theory

Authors: Vladimir Tolstykh

Abstract

Let $A$ be an infinitely generated free abelian group. We prove that the automorphism group $\aut A$ first-order interprets the full second-order theory of the set $|A|$ with no structure. In particular, this implies that the automorphism groups of two infinitely generated free abelian groups $A_1,A_2$ are elementarily equivalent if and only if the sets $|A_1|,|A_2|$ are second-order equivalent.

Keywords

free abelian group automorphism group first-order interpretation second-order theory elementary equivalence

Cite

@article{arxiv.math/0701752,
  title  = {What does the automorphism group of a free abelian group A know about A?},
  author = {Vladimir Tolstykh},
  journal= {arXiv preprint arXiv:math/0701752},
  year   = {2007}
}

Comments

A pre-publication preprint of a paper published in `2005

What does the automorphism group of a free abelian group A know about A?

Abstract

Keywords

Cite

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