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Groupes p -réduits

Marie-Paule Brameret (1962/1963)

Séminaire Dubreil. Algèbre et théorie des nombres

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.

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.

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 ) 2 α . We show:    Theorem 4.12. Let G be Abelian with |G| = γ. If either m(α) ≤ α and m ( α ) r 0 ( G ) γ 2 α , or α > ω and α ω r 0 ( G ) 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 ) m ( α ) .  Theorem 5.2(b). If G is divisible Abelian with 2 r 0 ( G ) 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 2 ; only six near isomorphism types of indecomposables if k = 3 ; and indecomposables of arbitrary large rank if k 4 .

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