A Note on the Growth of Davenport's constant.
A note on the isomorphism of modular group algebras of -mixed Abelian groups with divisible -components.
A note on the splitting length of a finite direct sum of mixed Abelian groups of rank one
-projective resolutions and an Azumaya theorem for a class of mixed abelian groups
A property of -groups
It is shown, under ZFC, that a -group has the interesting property of being -prebalanced in every torsion-free abelian group in which it is a pure subgroup. As a consequence, we obtain alternate proofs of some well-known theorems on -groups.
A quantitative aspect of non-unique factorizations: the Narkiewicz constants III
Let K be an algebraic number field with non-trivial class group G and be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let denote the number of non-zero principal ideals with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that behaves for x → ∞ asymptotically like . We prove, among other results, that for all integers n₁,n₂ with 1 < n₁|n₂.
A quantitative aspect of non-unique factorizations: the Narkiewicz constants II
Let K be an algebraic number field with non-trivial class group G and be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let denote the number of non-zero principal ideals with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that behaves, for x → ∞, asymptotically like . In this article, it is proved that for every prime p, , and it is also proved that if and m is large enough. In particular, it is shown that for...
A Rédei type factorization result for a special 2-group.
A remark on hyper-indecomposable groups
Un gruppo abeliano senza torsione ed indecomponibile è detto iperindecomponibile se tutti i sottogruppi propri del suo inviluppo iniettivo che lo contengono sono indecomponibili. In questo lavoro si caratterizza la classe dei gruppi iperindecomponibili per mezzo di loro proprietà locali. I gruppi iperindecomponibili omogenei sono caratterizzati tramite la proprietà «factor-splitting».
A remark on -systems in groups
A remark on subgroups of infinite index in Poincaré duality groups.
A result on -groups
A simple proof for a theorem of chase
A simple proof of Baer;s and Sato's theorems on lattice-isomorphisms between groups
A simple proof is given of a well-known result of the existance of lattice-isomorphisms between locally nilpotent quaternionfree modular groups and abelian groups.
A splitting criterion for Abelian groups
A theorem on direct products of Slender modules
A theorem on groups
A useful category for mixed Abelian groups.
Abelian Factorizations of Infinite Groups.
Abelian group extensions and the axiom of constructibility.