On the Structures of K2(ℤ[G]), G a Finite Abelian p-Group

Abstract

Let G be a finite abelian p-group, Γ the maximal ℤ-order of ℤ[G]. We prove that the 2-primary torsion subgroups of K2(ℤ[G]) and K2(Γ) are isomorphic when p ≡ 3, 5, 7 (mod 8), and [Formula: see text] is isomorphic to [Formula: see text] when p ≡ 2, 3, 5, 7. As an application, we give the structure of K2(ℤ[G]) for G a cyclic p-group or an elementary abelian p-group.