Results 151 to 160 of about 34,694 (181)

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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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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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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On a class of torsion-free abelian groups of finite rank

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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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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Splitting Mixed Groups of Finite Torsion-Free Rank

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 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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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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Multiplications on torsion-free groups of finite rank

Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры», 2023
Ekaterina Igorevna Kompantseva, Askar Tuganbaev   +1 more
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On the torsion-free ranks of finitely generated nilpotent groups and of their abelian subgroups

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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