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Displaying 81 – 100 of 127

On the Theory and Classification of Abelian p-Groups.

Paul Hill, Charles Megibben (1985)

Mathematische Zeitschrift

Properties of subgroups not containing their centralizers

Lemnouar Noui (2009)

Annales mathématiques Blaise Pascal

In this paper, we give a generalization of Baer Theorem on the injective property of divisible abelian groups. As consequences of the obtained result we find a sufficient condition for a group $G$ to express as semi-direct product of a divisible subgroup $D$ and some subgroup $H$ . We also apply the main Theorem to the $p$ -groups with center of index $p^{2}$ , for some prime $p$ . For these groups we compute $N_{c} (G)$ the number of conjugacy classes and $N_{a}$ the number of abelian maximal subgroups and $N_{n a}$ the number of nonabelian...

Pure subgroups

Ladislav Bican (2001)

Mathematica Bohemica

Let $λ$ be an infinite cardinal. Set $λ_{0} = λ$ , define $λ_{i + 1} = 2^{λ_{i}}$ for every $i = 0, 1, \dots$ , take $μ$ as the first cardinal with $λ_{i} < μ$ , $i = 0, 1, \dots$ and put $κ = {(μ^{ℵ_{0}})}^{+}$ . If $F$ is a torsion-free group of cardinality at least $κ$ and $K$ is its subgroup such that $F / K$ is torsion and $| F / K | \leq λ$ , then $K$ contains a non-zero subgroup pure in $F$ . This generalizes the result from a previous paper dealing with $F / K$ $p$ -primary.

Pure subgroups split

Ladislav Bican (1979)

Commentationes Mathematicae Universitatis Carolinae

Purely finitely generated Abelian groups

Ladislav Bican (1980)

Commentationes Mathematicae Universitatis Carolinae

Quasi-balanced torsion-free groups

H. Pat Goeters, William Ullery (1998)

Commentationes Mathematicae Universitatis Carolinae

An exact sequence $0 \to A \to B \to C \to 0$ of torsion-free abelian groups is quasi-balanced if the induced sequence $0 \to 𝐐 \otimes Hom (X, A) \to 𝐐 \otimes Hom (X, B) \to 𝐐 \otimes Hom (X, C) \to 0$ is exact for all rank-1 torsion-free abelian groups $X$ . This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which $C$ is a Butler group. The special case where $B$ is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced...

Quasibases of $p$ -groups

Otto Mutzbauer, Elias Toubassi (1999)

Rendiconti del Seminario Matematico della Università di Padova

Quasi-essential subsocles of Abelian p-groups

Moore, J. Douglas (1979)

Portugaliae mathematica

Regularität in torsionsfreien abelschen Gruppen

Edgar Müller, Otto Mutzbauer (1992)

Czechoslovak Mathematical Journal

Regulierende Untergruppen und der Regulator fast vollständig zerlegbarer Gruppen

Bernhard Frey, Otto Mutzbauer (1992)

Rendiconti del Seminario Matematico della Università di Padova

Schichtengleiche Gewichte und Butlergruppen

Edgar Müller, Otto Mutzbauer (1997)

Czechoslovak Mathematical Journal

Self-pseudoprojective completely decomposable Abelian groups.

Gardner, B.J. (1998)

Mathematica Pannonica

Separable and vector groups whose projectively invariant subgroups are fully invariant.

Chekhlov, A.R. (2009)

Sibirskij Matematicheskij Zhurnal

Separable mixed groups

Charles K. Megibben (1980)

Commentationes Mathematicae Universitatis Carolinae

Some generalizations of torsion-free Crawley groups

Brendan Goldsmith, Fatemeh Karimi, Ahad Mehdizadeh Aghdam (2013)

Czechoslovak Mathematical Journal

In this paper we investigate two new classes of torsion-free Abelian groups which arise in a natural way from the notion of a torsion-free Crawley group. A group $G$ is said to be an Erdős group if for any pair of isomorphic pure subgroups $H, K$ with $G / H ≅ G / K$ , there is an automorphism of $G$ mapping $H$ onto $K$ ; it is said to be a weak Crawley group if for any pair $H, K$ of isomorphic dense maximal pure subgroups, there is an automorphism mapping $H$ onto $K$ . We show that these classes are extensive and pay attention to...

Splitting in abelian groups

Ladislav Bican (1978)

Czechoslovak Mathematical Journal

Splittings of infinite abelian group.

Steve Galovich, Jack Goldfeather (1986)

Aequationes mathematicae

Splittings of infinite abelian group. (Short Communication).

Steve Galovich, Jack Goldfeather (1986)

Aequationes mathematicae

Square subgroups of rank two abelian groups

A. M. Aghdam, A. Najafizadeh (2009)

Colloquium Mathematicae

Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.

Strong $𝒮$ -groups

Ulrich Albrecht, H. Goeters (1999)

Colloquium Mathematicae

Currently displaying 81 – 100 of 127

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