منابع مشابه
Universal Abelian Groups
We examine the existence of universal elements in classes of infinite abelian groups. The main method is using group invariants which are defined relative to club guessing sequences. We prove, for example: Theorem: For n ≥ 2, there is a purely universal separable p-group in אn if, and only if, 20 ≤ אn. §0 Introduction In this paper “group” will always mean “infinite abelian group”, and “cardina...
متن کاملnon-divisibility for abelian groups
Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...
متن کاملKulikov’s problem on universal torsion-free abelian groups revisited
Let T be a torsion abelian group. We consider the class of all torsion-free abelian groups G satisfying Ext(G,T ) = 0 and search for λ-universal objects in this class. We show that for certain T there is no ω-universal group. However, for uncountable cardinals λ there is always a λ-universal group if we assume (V = L). Together with results by the second author this solves completely a problem ...
متن کاملNon-existence of Universal Members in Classes of Abelian Groups
Abstract. We prove that if μ < λ = cf(λ) < μ0 , then there is no universal reduced torsion free abelian group of cardinality λ. Similarly if א0 < λ < 20 . We also prove that if iω < μ < λ = cf(λ) < μ0 , then there is no universal reduced separable abelian p-group in λ. We also deal with the class of א1-free abelian group. (Note: both results fail if (a) λ = λ0 or if (b) λ is strong limit, cf(μ)...
متن کاملKulikov’s problem on universal torsion-free abelian groups
Let T be an abelian group and λ an uncountable regular cardinal. We consider the question of whether there is a λ-universal group G∗ among all torsion-free abelian groups G of cardinality less than or equal to λ satisfying Ext(G, T ) = 0. Here G∗ is said to be λ-universal for T if, whenever a torsionfree abelian group G of cardinality less than or equal to λ satisfies Ext(G, T ) = 0, then there...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 1995
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02762072