Separative Cancellation and Multiple Isomorphism in Torsion-Free Abelian Groups
نویسندگان
چکیده
منابع مشابه
Uniquely Transitive Torsion-free Abelian Groups
We will answer a question raised by Emmanuel Dror Farjoun concerning the existence of torsion-free abelian groups G such that for any ordered pair of pure elements there is a unique automorphism mapping the first element onto the second one. We will show the existence of such a group of cardinality λ for any successor cardinal λ = μ+ with μ = μ0.
متن کاملJump degrees of torsion-free abelian groups
We show, for each computable ordinal α and degree a > 0(α), the existence of a torsion-free abelian group with proper αth jump degree a.
متن کاملThe Classification of Torsion-free Abelian Groups of Finite Rank up to Isomorphism and up to Quasi-isomorphism
We prove that the isomorphism and quasi-isomorphism relations on the p-local torsion-free abelian groups of fixed finite rank n are incomparable with respect to Borel reducibility.
متن کاملThe Isomorphism Problem for Torsion - Free Abelian Groups Is Analytic Complete
We prove that the isomorphism problem for torsion-free Abelian groups is as complicated as any isomorphism problem could be in terms of the analytical hierarchy, namely Σ1 complete.
متن کاملThe isomorphism problem for residually torsion-free nilpotent groups
Both the conjugacy and isomorphism problems for finitely generated nilpotent groups are recursively solvable. In some recent work, the first author, with a tiny modification of work in the second author’s thesis, proved that the conjugacy problem for finitely presented, residually torsion-free nilpotent groups is recursively unsolvable. Here we complete the algorithmic picture by proving that t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7990