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

Characterizing automorphism groups of ordered abelian groups

We characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of abelian groups.

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'.

周期阿贝尔群的自同态环与自同构群的初等等价

Elementary equivalence of endomorphism rings and automorphism groups of periodic Abelian groups

该研究探讨周期阿贝尔群的自同态环与自同构群的初等等价问题，给出了自同态环初等等价的充要条件，并针对特定周期阿贝尔群刻画了自同构群初等等价的等价条件。

有序阿贝尔群自同构的合并性质

The Amalgamation Property for automorphisms of ordered abelian groups

证明带有自同构的有序阿贝尔群范畴具有合并性质，推出其归纳理论在正逻辑意义下是NIP的，并初步发展了正逻辑框架。

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(withdrawn.)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.

简单马尔采夫代数布尔幂自同构群中的丰富泛型

Ample generics in automorphism groups of Boolean powers of simple Mal'cev algebras

研究有限简单马尔采夫代数布尔幂自同构群的丰富泛型，通过分阿贝尔和非阿贝尔情形证明，利用模表示、\(n\) - 系统理论及群分解等，还得到\(\mathrm{Homeo}\, 2^\omega\)中逐点稳定子有丰富泛型的结果。