K 2 of a Quotient Ring of ℤG

Abstract

Let G be a finite abelian group and Γ the maximal ℤ-order of ℚG, an explicit description of Γ is given. When G is an elementary abelian p-group or a cyclic p-group, we give a lower bound for the order of K 2(ℤG/|G|Γ). For a finite abelian group G, we prove that K 2(ℤG/|G|Γ) is trivial if and only if |G| is square-free. Some discussions about the order of K 2(ℤG) are also given, especially for G a finite p-group when p is a regular prime.