Results 171 to 180 of about 2,880 (211)
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Actions of abelian groups on groups
Journal of Group Theory, 2007Let G be a group and A a finitely generated abelian subgroup of Aut(G). If G is the union of a finitely many A-orbits then G is finite.
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Mathematical Notes, 2020
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Kolenova, E. M., Pushkova, T. A.
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Kolenova, E. M., Pushkova, T. A.
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Topology and its Applications, 2018
An abelian group \(N\) equipped with the discrete topology is called cancellable if for any two abelian topological groups \(G\) and \(H\), the product group \(G \times N \cong H \times N\) if and only if \(G \cong H\), where the symbol \(\cong\) means the topological isomorphism the between groups.
Peng, De Kui, He, Wei
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An abelian group \(N\) equipped with the discrete topology is called cancellable if for any two abelian topological groups \(G\) and \(H\), the product group \(G \times N \cong H \times N\) if and only if \(G \cong H\), where the symbol \(\cong\) means the topological isomorphism the between groups.
Peng, De Kui, He, Wei
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Asian-European Journal of Mathematics, 2008
A problem for Abelian groups is formulated with motivations from the theory of constant weight codes. The problem is solved for the case (ℤ2)r.
Katona, Gyula, Makar-Limanov, Leonid
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A problem for Abelian groups is formulated with motivations from the theory of constant weight codes. The problem is solved for the case (ℤ2)r.
Katona, Gyula, Makar-Limanov, Leonid
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Journal of Algebra and Its Applications, 2010
An R-module RM is called morphic if M/ im α ≅ ker α for every endomorphism α of M, that is, if the dual of the Noether isomorphism theorem holds. Mostly all morphic Z-modules are determined leaving open some classes of nonsplitting mixed groups, which actually cannot be completely characterized.
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An R-module RM is called morphic if M/ im α ≅ ker α for every endomorphism α of M, that is, if the dual of the Noether isomorphism theorem holds. Mostly all morphic Z-modules are determined leaving open some classes of nonsplitting mixed groups, which actually cannot be completely characterized.
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Canadian Journal of Mathematics, 1967
The difficulties encountered in the theory of mixed Abelian groups can become decidedly less complex, if it is possible to reduce the question to mixed groups whose torsion subgroup is 𝒫-primary. Call such a group a p-mixed group. In §1 we show that the splitting problem for a mixed group is reducible to the same problem for certain associated 𝒫-mixed ...
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The difficulties encountered in the theory of mixed Abelian groups can become decidedly less complex, if it is possible to reduce the question to mixed groups whose torsion subgroup is 𝒫-primary. Call such a group a p-mixed group. In §1 we show that the splitting problem for a mixed group is reducible to the same problem for certain associated 𝒫-mixed ...
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Journal of Mathematical Sciences, 2006
The paper deals with torsion free Abelian groups of finite rank and provides relations between pureness, servantness, and quasi-decompositions for such groups. In particular, endopure and servant submodules for Abelian groups of rank 3 and for strongly indecomposable groups are classified.
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The paper deals with torsion free Abelian groups of finite rank and provides relations between pureness, servantness, and quasi-decompositions for such groups. In particular, endopure and servant submodules for Abelian groups of rank 3 and for strongly indecomposable groups are classified.
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Canadian Journal of Mathematics, 1957
Throughout this note all groups areabelian, written additively. We refer to Kurosh (8; 9) for notation, terminology and theorems used without reference. We recall the notion of aserving subgroup(or pure subgroup)of a group. This is a subgroupin which for every natural numbernevery equationnx = s, s ∊can be solved provided that it can be solved in. Ifis
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Throughout this note all groups areabelian, written additively. We refer to Kurosh (8; 9) for notation, terminology and theorems used without reference. We recall the notion of aserving subgroup(or pure subgroup)of a group. This is a subgroupin which for every natural numbernevery equationnx = s, s ∊can be solved provided that it can be solved in. Ifis
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Israel Journal of Mathematics, 1979
We continue the investigation from [10], [11], [12] on uncountable abelian groups. This paper tends more to group theory and was motivated by Nunke’s statement (in [9]) that Whitehead problem, rephrased properly, is not solved yet.
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We continue the investigation from [10], [11], [12] on uncountable abelian groups. This paper tends more to group theory and was motivated by Nunke’s statement (in [9]) that Whitehead problem, rephrased properly, is not solved yet.
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