EuDML | Browse

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.

Gruppi monotóni di successioni intere

L. Fuchs, L. Salce (1976)

Rendiconti del Seminario Matematico della Università di Padova

Hajós' theorem and the partition lemma.

Szabó, Sándor (2005)

Beiträge zur Algebra und Geometrie

Hereditary endomorphism rings of mixed Abelian groups.

Krylov, P.A. (2002)

Sibirskij Matematicheskij Zhurnal

Homology and Direct Sums of Countable Abelian Groups.

R.J. Nunke (1967)

Mathematische Zeitschrift

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

Imposing psendocompact group topologies on Abeliau groups

W. Comfort, I. Remus (1993)

Fundamenta Mathematicae

The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, $m (α) \leq 2^{α}$ . We show: Theorem 4.12. Let G be Abelian with |G| = γ. If either m(α) ≤ α and m $(α) \leq r_{0} (G) \leq γ \leq 2^{α}$ , or α > ω and $α^{ω} \leq r_{0} (G) \leq 2^{α}$ , then G admits a pseudocompact group topology of weight α. Theorem 4.15. Every connected, pseudocompact Abelian group G with wG = α ≥ ω satisfies $r_{0} (G) \geq m (α)$ . Theorem 5.2(b). If G is divisible Abelian with $2^{r_{0} (G)} \leq γ$ , then G admits at most $2^{γ}$ -many...

Indecomposable (1,3)-groups and a matrix problem

David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak (2013)

Czechoslovak Mathematical Journal

Almost completely decomposable groups with a critical typeset of type $(1, 3)$ and a $p$ -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient $p^{k}$ , either no indecomposables if $k \leq 2$ ; only six near isomorphism types of indecomposables if $k = 3$ ; and indecomposables of arbitrary large rank if $k \geq 4$ .

Currently displaying 221 – 240 of 701

Previous Page 12 Next