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Displaying 21 – 40 of 57

Growth functions for some uniformly amenable groups

Janusz Dronka, Bronislaw Wajnryb, Paweł Witowicz, Kamil Orzechowski (2017)

Open Mathematics

We present a simple constructive proof of the fact that every abelian discrete group is uniformly amenable. We improve the growth function obtained earlier and find the optimal growth function in a particular case. We also compute a growth function for some non-abelian uniformly amenable group.

Hereditary endomorphism rings of mixed Abelian groups.

Krylov, P.A. (2002)

Sibirskij Matematicheskij Zhurnal

Homomorphisms between $A$ -projective Abelian groups and left Kasch-rings

Ulrich F. Albrecht, Jong-Woo Jeong (1998)

Czechoslovak Mathematical Journal

Glaz and Wickless introduced the class $G$ of mixed abelian groups $A$ which have finite torsion-free rank and satisfy the following three properties: i) $A_{p}$ is finite for all primes $p$ , ii) $A$ is isomorphic to a pure subgroup of $Π_{p} A_{p}$ , and iii) $H o m (A, t A)$ is torsion. A ring $R$ is a left Kasch ring if every proper right ideal of $R$ has a non-zero left annihilator. We characterize the elements $A$ of $G$ such that $E (A) / t E (A)$ is a left Kasch ring, and discuss related results.

Hulls of mixed modules with finite quotient $p$ -rank

Otto Mutzbauer, Elias Toubassi (1999)

Czechoslovak Mathematical Journal

Isomorphism of commutative group algebras of $p$ -mixed splitting groups over rings of characteristic zero

Peter Vassilev Danchev (2006)

Mathematica Bohemica

Suppose $G$ is a $p$ -mixed splitting abelian group and $R$ is a commutative unitary ring of zero characteristic such that the prime number $p$ satisfies $p \notin inv (R) \cup zd (R)$ . Then $R (H)$ and $R (G)$ are canonically isomorphic $R$ -group algebras for any group $H$ precisely when $H$ and $G$ are isomorphic groups. This statement strengthens results due to W. May published in J. Algebra (1976) and to W. Ullery published in Commun. Algebra (1986), Rocky Mt. J. Math. (1992) and Comment. Math. Univ. Carol. (1995).

Isomorphism of modular group algebras of direct sums of torsion-complete abelian $p$ -groups

Peter V. Danchev (1999)

Rendiconti del Seminario Matematico della Università di Padova

Isotype knice subgroups of global Warfield groups

Charles K. Megibben, William Ullery (2006)

Czechoslovak Mathematical Journal

If $H$ is an isotype knice subgroup of a global Warfield group $G$ , we introduce the notion of a $k$ -subgroup to obtain various necessary and sufficient conditions on the quotient group $G / H$ in order for $H$ itself to be a global Warfield group. Our main theorem is that $H$ is a global Warfield group if and only if $G / H$ possesses an $H (ℵ_{0})$ -family of almost strongly separable $k$ -subgroups. By an $H (ℵ_{0})$ -family we mean an Axiom 3 family in the strong sense of P. Hill. As a corollary to the main theorem, we are able to characterize...

Isotype subgroups of mixed groups.

Megibben, Charles, Ullery, William (2001)

Commentationes Mathematicae Universitatis Carolinae

Isotype subgroups of mixed groups

Charles K. Megibben, William Ullery (2001)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we initiate the study of various classes of isotype subgroups of global mixed groups. Our goal is to advance the theory of $Σ$ -isotype subgroups to a level comparable to its status in the simpler contexts of torsion-free and $p$ -local mixed groups. Given the history of those theories, one anticipates that definitive results are to be found only when attention is restricted to global $k$ -groups, the prototype being global groups with decomposition bases. A large portion of this paper is...

$N$ -pure-high subgroups of abelian groups

Jindřich Bečvář (1985)

Acta Universitatis Carolinae. Mathematica et Physica

Nice bases for mixed and torsion-free Abelian groups.

Danchev, Peter (2010)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Notes on mixed groups II

Phillip Schultz (1986)

Rendiconti del Seminario Matematico della Università di Padova

On extensions of bounded subgroups in Abelian groups

S. S. Gabriyelyan (2014)

Commentationes Mathematicae Universitatis Carolinae

It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups $H$ of an infinite Abelian group $G$ , for which there is an infinite subgroup $G_{0}$ of $G$ containing $H$ such that $G_{0}$ has a special decomposition into a direct sum which takes into account the properties of $G$ , and which induces a natural decomposition of $H$ into a direct sum of finite subgroups.

On Fuchs' problem 76.

Birge Zimmermann-Huisgen (1979)

Journal für die reine und angewandte Mathematik

On p-Local Abelian Groups with Decomposititon Bases.

Mark Lane (1989)

Mathematische Zeitschrift

On the Cayley-Hamilton property in abelian groups.

Militello, Robert R. (1992)

International Journal of Mathematics and Mathematical Sciences

Projektivitätstypen torsionsfreier abelscher Gruppen vom Rang 1

Uwe Ostendorf (1991)

Rendiconti del Seminario Matematico della Università di Padova

Pure subgroups split

Ladislav Bican (1979)

Commentationes Mathematicae Universitatis Carolinae

Self- $c$ -injective abelian groups

Simion Breaz, Grigore Călugăreanu (2006)

Rendiconti del Seminario Matematico della Università di Padova

Self-small products of abelian groups

Josef Dvořák, Jan Žemlička (2022)

Commentationes Mathematicae Universitatis Carolinae

Let $A$ and $B$ be two abelian groups. The group $A$ is called $B$ -small if the covariant functor $Hom (A, -)$ commutes with all direct sums $B^{(κ)}$ and $A$ is self-small provided it is $A$ -small. The paper characterizes self-small products applying developed closure properties of the classes of relatively small groups. As a consequence, self-small products of finitely generated abelian groups are described.

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