A certain property of abelian groups
A characterization of countable Butler groups
A characterization of Ext(G,ℤ) assuming (V = L)
We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence of cardinals satisfying (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that equals the p-rank of Ext(G,ℤ) for every...
A characterization of minimal zero-sequences of index one in finite cyclic groups.
A characterization of sequences with the minimum number of k-sums modulo k
Let G be an additive abelian group of order k, and S be a sequence over G of length k+r, where 1 ≤ r ≤ k-1. We call the sum of k terms of S a k-sum. We show that if 0 is not a k-sum, then the number of k-sums is at least r+2 except for S containing only two distinct elements, in which case the number of k-sums equals r+1. This result improves the Bollobás-Leader theorem, which states that there are at least r+1 k-sums if 0 is not a k-sum.
A characterization of subgroup lattices of finite abelian groups.
A class of torsion-free abelian groups characterized by the ranks of their socles
Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket -module is tensor a bracket group.
A closed category of reflexive topological abelian groups
A coarse convergence group need not be precompact
A consequence of a theorem of L. Fuchs
A constructive proof that every 3-generated l-group is ultrasimplicial
We discuss the ultrasimplicial property of lattice-ordered abelian groups and their associated MV-algebras. We give a constructive proof of the fact that every lattice-ordered abelian group generated by three elements is ultrasimplicial.
A direct factor theorem for commutative group algebras
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 .
A generalization of a theorem of F. Richman and C. P. Walker
A generalization of a theorem of R. Baer
A Generalization of Baer's Splitting problem on Abelian groups.
A generalization of separable torsion-free abelian groups
A geometric invariant for modules over an Abelian group.
A Group with Torsion-Free 2-Divisible Homology and Cappell's Result on the Novikov Conjecture.
A Guichard theorems on connected monothetic groups
A Hajós type result on factoring finite abelian groups by subsets. II
It is proved that if a finite abelian group is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be periodic. This result generalizes Hajós's factorization theorem.