New Criteria for Freeness in Abelian Groups
نویسندگان
چکیده
منابع مشابه
NEW CRITERIA FOR FREENESS IN ABELIAN GROUPS . H ( i )
A new criterion is established for an abelian group to be free. The criterion is in terms of an ascending chain of free subgroups and is dependent upon a new class of torsion-free groups. The result leads to the construction, for each positive integer n, of a group G of cardinality K that is not free but is X -free. A conjecture in infinitary logic concern71 n ing free abelian groups is also ve...
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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...
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We prove two theorems of the type of Dieudonné for the classes of p-torsion n-Σ-groups and weakly n-summable groups, respectively. These claims extend the classical Dieudonné criterion (Portugal. Math., 1952) and Honda criterion (Comment. Math. Univ. St. Pauli, 1964) as well as generalize recent results of ours in (Acta Math. Univ. Ostrav., 2006; 2007) and (Alg. Colloq., 2008). Introduction and...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.2307/1996530