Results 181 to 190 of about 557 (225)

On Torsion-Free Groups of Finite Rank

Canadian Journal of Mathematics, 1984
This 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 ...
Akbar Rhemtulla, David Meier
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On a class of torsion-free abelian groups of finite rank [PDF]

Mathematical Notes, 1994
A class of torsion free finite rank Abelian groups is characterized in this paper. The class can be treated as a generalization of Murley's \(\mathcal E\)-group class. The results of \textit{A. Fomin}'s paper [Algebra Logika 26, No. 1, 63-83 (1987; Zbl 0638.20030)] are applied.
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FINITE AUTOMORPHISM GROUPS OF TORSION-FREE ABELIAN GROUPS OF FINITE RANK

Mathematics of the USSR-Izvestiya, 1989
A 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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Splitting Mixed Groups of Finite Torsion-Free Rank [PDF]

Communications in Algebra, 2004
Abstract First, we give a necessary and sufficient condition for torsion-free finite rank subgroups of arbitrary abelian groups to be purifiable. An abelian group G is said to be a strongly ADE decomposable group if there exists a purifiable T(G)-high subgroup of G. We use a previous result to characterize ADE decomposable groups of finite torsion-free
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On quasidecomposable finite rank torsion-free Abelian groups

Siberian Mathematical Journal, 1998
The 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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Torsion-free Abelian groups of finite rank without nilpotent endomorphisms [PDF]

Siberian Mathematical Journal, 1988
See the review in Zbl 0645.20033.
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Duality in some classes of torsion-free Abelian groups of finite rank [PDF]

Siberian Mathematical Journal, 1987
Let \(\sigma\), \(\tau\) be a pair of types of torsion-free (abelian) groups of rank 1 which are determined by characteristics \((k_ p)\), \((m_ p)\) such that \(k_ p\leq m_ p\) for all primes \(p\). A torsion-free group \(A\) of finite rank \(n\) belongs to the class \(D^{\tau}_{\sigma}\) iff there exists a free subgroup \(J\) of rank \(n\) of \(A ...
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Balanced projective and cobalanced injective torsion free groups of finite rank

Acta Mathematica Hungarica, 1985
Let TF denote the category of torsion free abelian groups of finite rank and homomorphisms. The authors prove that a group A in TF is completely indecomposable if and only if A is projective with respect to all balanced exact sequences in TF if and only if A is injective with respect to all co-balanced exact sequences in TF. Using different techniques,
W. Wickless, C. Vinsonhaler
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Radical modules over hyperabelian groups of finite torsion-free rank [PDF]

jgth, 1998
This paper continues the author's work on radical modules over infinite groups satisfying some finiteness condition, where a module \(M\) over a group \(G\) is called radical if there exists a surjective derivation from \(G\) onto \(M\). Prototypes of such modules are radical rings in the sense of Jacobson, regarded as modules over their adjoint groups.
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Direct decompositions of torsion-free Abelian groups of finite rank

Journal of Soviet Mathematics, 1985
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 132, 17-25 (Russian) (1983; Zbl 0524.20029).
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