A Group with Torsion-Free 2-Divisible Homology and Cappell's Result on the Novikov Conjecture.
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.
We prove that pure subgroups of thick Abelian -groups which are modulo countable are again thick. This generalizes a result due to Megibben (Michigan Math. J. 1966). Some related results are also established.
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.