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 .
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...
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...
Page 1