Splittings of Poincaré Duality Groups.
Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.
Our aim in this paper is to study the concept of stability for acts over monoids and in the process develop connections with flatness properties of acts and with some of the current techniques and construction used in the homological classification of monoids. We also present new proofs of some results relating to torsion free acts over monoids and to the embeddability of semigroup amalgams.
We determine the stable cohomology groups ( of the alternating groups for all integers n and i, and all odd primes p.