Suppose is a prime number and is a commutative ring with unity of characteristic 0 in which is not a unit. Assume that and are -primary abelian groups such that the respective group algebras and are -isomorphic. Under certain restrictions on the ideal structure of , it is shown that and are isomorphic.
Suppose is a field of characteristic and is a -primary abelian -group. It is shown that is a direct factor of the group of units of the group algebra .
An exact sequence of torsion-free abelian groups is quasi-balanced if the induced sequence is exact for all rank-1 torsion-free abelian groups . This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which is a Butler group. The special case where is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced...
In this paper, we initiate the study of various classes of isotype subgroups of global mixed groups. Our goal is to advance the theory of -isotype subgroups to a level comparable to its status in the simpler contexts of torsion-free and -local mixed groups. Given the history of those theories, one anticipates that definitive results are to be found only when attention is restricted to global -groups, the prototype being global groups with decomposition bases. A large portion of this paper is...
If is an isotype knice subgroup of a global Warfield group , we introduce the notion of a -subgroup to obtain various necessary and sufficient conditions on the quotient group in order for itself to be a global Warfield group. Our main theorem is that is a global Warfield group if and only if possesses an -family of almost strongly separable -subgroups. By an -family we mean an Axiom 3 family in the strong sense of P. Hill. As a corollary to the main theorem, we are able to characterize...
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