Results 201 to 210 of about 35,005 (235)
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Extensions of torsion-free Abelian groups of finite rank
Archiv der Mathematik, 1972openaire +3 more sources
On Torsion-Free Groups of Finite Rank
Canadian Journal of Mathematics, 1984This paper deals with two conditions which, when stated, appear similar, but when applied to finitely generated solvable groups have very different effect. We first establish the notation before stating these conditions and their implications. If H is a subgroup of a group G, let denote the setWe say G has the isolator property if is a subgroup for ...
Meier, David, Rhemtulla, Akbar
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A Class of Torsion-Free Abelian Groups of Finite Rank
Proceedings of the London Mathematical Society, 1965openaire +4 more sources
Torsion-Free Abelian Groups of Finite Rank with Marked Bases
Journal of Mathematical Sciences, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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FINITE AUTOMORPHISM GROUPS OF TORSION-FREE ABELIAN GROUPS OF FINITE RANK
Mathematics of the USSR-Izvestiya, 1989A well-known result of Jónsson states that each torsion-free group G of finite rank has a quasi-direct decomposition i.e. a subgroup A of finite index which is a direct sum of pure strongly indecomposable subgroups. For such a group several quasi-direct decompositions do exist all being quasi-isomorphic but generally not isomorphic.
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Totally Transitive Torsion-Free Groups of Finite p-Rank
Algebra and Logic, 2001A 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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On quasidecomposable finite rank torsion-free Abelian groups
Siberian Mathematical Journal, 1998The author obtains two types of quasidecompositions for a finite rank torsion-free Abelian group \(G\). Using them, he proves pure semisimplicity of the module \(_EG\) in a particular case and obtains a criterion for pure semisimplicity of the module \(_EG\) in the general case.
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Self-Cancellation of Torsion-Free Abelian Groups of Finite Rank
Journal of Mathematical Sciences, 2002An 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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Direct decompositions of torsion-free Abelian groups of finite rank
Journal of Soviet Mathematics, 1990See the review in Zbl 0631.20045.
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Soluble Groups of Type (FP)∞ have Finite Torsion-Free Rank
Bulletin of the London Mathematical Society, 1993A 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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