Results 191 to 200 of about 557 (225)

Self-Cancellation of Torsion-Free Abelian Groups of Finite Rank

Journal of Mathematical Sciences, 2002
An Abelian group \(A\) is said to have self-cancellation if \(A\oplus A\cong A\oplus B\) implies \(A\cong B\). A very simple example of a rank 4 torsion-free Abelian group without the self-cancellation property is constructed. The construction is based on the author's criterion [Algebra Anal. 7, No. 6, 33-78 (1995); corrections ibid. 11, No. 4, 222-224
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Torsion-Free Abelian Groups of Finite Rank with Marked Bases

Journal of Mathematical Sciences, 2021
We define a one-to-one correspondence between torsion-free Abelian groups of finite rank with marked bases and finite sequences of elements of finitely presented modules over the ring of polyadic numbers. This correspondence is a duality of two categories.
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On the torsion-free ranks of finitely generated nilpotent groups and of their abelian subgroups [PDF]

Journal of Group Theory, 2004
Denote by \(f(n)\) the greatest integer \(h\) such that there exists a finitely generated nilpotent group of torsion-free rank \(h\) such that the torsion-free ranks of all Abelian subgroups of this group are not greater than \(n\). The author proves that the function \(f(n)\) satisfies the inequality \(f(n)\geq\tfrac18(n^2-4)+n\). Proving this theorem,
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Direct decompositions of torsion-free Abelian groups of finite rank

Journal of Soviet Mathematics, 1990
See the review in Zbl 0631.20045.
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Totally Transitive Torsion-Free Groups of Finite p-Rank

Algebra and Logic, 2001
A torsion-free Abelian group \(A\) is a totally transitive group if any two elements \(a,b\in A\) with the characteristic condition \(\chi_A(a)\leq\chi_A(b)\) (\(\chi_A(a)=\chi_A(b)\)) are endomorphic (automorphic) conjugate elements, i.e., there is an endomorphism (automorphism) \(f\) such that \(fa=b\).
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Categories of Mixed and Torsion-Free Finite Rank Abelian Groups [PDF]

, 1995
In this paper “group” always means “abelian group”. For a group G let T = T(G) be the torsion part and, for a prime p, let T p = T p (G), be the p-torsion part of G.
Alexander Fomin, W. Wickless
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Torsion-free abelian α-irreducible groups of finite rank

Communications in Algebra, 1994
If F is a free abelian group of finite rank and α is an endomorphism or an automorphism of its divisible hull, then the α‐ hull is determined, i.e. the minimal torsion-free abelian group with this endomorphism a. Torsion-free abelian groups of finite rank are called α-irreducible if their divisible hull is α-irreducible for an automorphism a.
Alexander A. Fomin, Otto Mutzbauer
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On the Complexity of the Classification Problem for Torsion-Free Abelian Groups of Finite Rank

Bulletin of Symbolic Logic, 2001
In this paper, we shall discuss some recent contributions to the project [15, 14, 2, 18, 22, 23] of explaining why no satisfactory system of complete invariants has yet been found for the torsion-free abelian groups of finite rank n ≥ 2. Recall that, up to isomorphism, the torsion-free abelian groups of rank n are exactly the additive subgroups of the ...
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Direct decompositions of torsion-free homogeneous Abelian groups of finite rank

Lithuanian Mathematical Journal, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Soluble Groups of Type (FP)∞ have Finite Torsion-Free Rank

Bulletin of the London Mathematical Society, 1993
A group \(G\) is said to be of type \((FP)_ \infty\) over a non-zero commutative ring \(k\) if there is an exact sequence of \(ZG\)-modules \(P_ i\) of the form \(\dots \to P_ n \to \dots \to P_ 1 \to P_ 0 \to k\) with the modules \(P_ 0,P_ 1,\dots,P_ n,\dots\) finitely generated and projective. (Here \(k\) also denotes the trivial \(ZG\)-module).
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