The classification problem for torsion-free abelian groups of finite rank
نویسندگان
چکیده
منابع مشابه
On the complexity of the classification problem for torsion-free abelian groups of finite rank
In 1937, Baer [5] introduced the notion of the type of an element in a torsion-free abelian group and showed that this notion provided a complete invariant for the classification problem for torsion-free abelian groups of rank 1. Since then, despite the efforts of such mathematicians as Kurosh [23] and Malcev [25], no satisfactory system of complete invariants has been found for the torsion-fre...
متن کاملBorel superrigidity and the classification problem for the torsion-free abelian groups of finite rank
In 1937, Baer solved the classification problem for the torsion-free abelian groups of rank 1. Since then, despite the efforts of many mathematicians, no satisfactory solution has been found of the classification problem for the torsion-free abelian groups of rank n ≥ 2. So it is natural to ask whether the classification problem for the higher rank groups is genuinely difficult. In this article...
متن کاملThe Classification Problem for Torsion-free Abelian Groups of Finite Rank
In 1937, Baer [5] introduced the notion of the type of an element in a torsion-free abelian group and showed that this notion provided a complete invariant for the classification problem for torsion-free abelian groups of rank 1. Since then, despite the efforts of such mathematicians as Kurosh [23] and Malcev [25], no satisfactory system of complete invariants has been found for the torsion-fre...
متن کاملTHE CLASSIFICATION PROBLEM FOR p-LOCAL TORSION-FREE ABELIAN GROUPS OF FINITE RANK
Let n ≥ 3. We prove that if p 6= q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank n are incomparable with respect to Borel reducibility.
متن کاملThe Classification Problem for S-local Torsion-free Abelian Groups of Finite Rank
Suppose that n ≥ 2 and that S, T are sets of primes. Then the classification problem for the S-local torsion-free abelian groups of rank n is Borel reducible to the classification problem for the T -local torsion-free abelian groups of rank n if and only if S ⊆ T .
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2002
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-02-00409-5