Separable mixed groups
Some generalizations of torsion-free Crawley groups
In this paper we investigate two new classes of torsion-free Abelian groups which arise in a natural way from the notion of a torsion-free Crawley group. A group is said to be an Erdős group if for any pair of isomorphic pure subgroups with , there is an automorphism of mapping onto ; it is said to be a weak Crawley group if for any pair of isomorphic dense maximal pure subgroups, there is an automorphism mapping onto . We show that these classes are extensive and pay attention to...
Splitting in abelian groups
Subgroups of the basic subgroup in a modular group ring
Sylow P-Subgroups of Abelian Group Rings
2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.Let PG be the abelian modular group ring of the abelian group G over the abelian ring P with 1 and prime char P = p. In the present article,the p-primary components Up(PG) and S(PG) of the groups of units U(PG) and V(PG) are classified for some major classes of abelian groups. Suppose K is a first kind field with respect to p in char K ≠ p and A is an abelian p-group. In the present work, the p-primary...
Tensor product and quasi-splitting of Abelian groups
The nonseparability of simply presented mixed groups
It is demonstrated that an isotype subgroup of a simply presented abelian group can be simply presented without being a separable subgroup. In particular, the conjecture based on a variety of special cases that Warfield groups are absolutely separable is disproved.
The pseudorational rank of an Abelian group.
The splitting of the tensor product of two mixed abelian groups of rank one
Trivial units in commutative group algebras.
Uniqueness theorems for global mixed groups.
Various local global principles for abelian groups.
We discuss local global principles for abelian groups by examining the adjoint functor pair obtained by (left adjoint) sending an abelian group A to the local diagram L(A) = {Z(p) ⊗ A → Q ⊗ A} and (right adjoint) applying the inverse limit functor to such diagrams; p runs through all integer primes. We show that the natural map A → lim L(A) is an isomorphism if A has torsion at only finitely many primes. If A is fixed we answer the genus problem of identifying all those groups B for which the local...
Warfield Invariants in Abelian Group Algebras
Warfield invariants in abelian group rings.
Let R be a perfect commutative unital ring without zero divisors of char(R) = p and let G be a multiplicative abelian group. Then the Warfield p-invariants of the normed unit group V (RG) are computed only in terms of R and G. These cardinal-to-ordinal functions, combined with the Ulm-Kaplansky p-invariants, completely determine the structure of V (RG) whenever G is a Warfield p-mixed group.
О прямых произведениях абелевых групп
Разрешимые F-факторизуемые группы
Центр кольца эндоморфизмов расщепляющейся смешанной абелевой группы