A note on one decomposition of the 2-primary part of K 2(ℤ[C p × (C 2) n

Abstract

Let Cn be a cyclic group of order n. We investigate K 2 of integral group rings via the Mayer-Vietoris sequence, and give a decomposition of the 2-primary torsion subgroup of K 2 ( Z [ C p × ( C 2 ) n ] ) for any prime p ≡ 3 , 5 , 7 ( mod 8 ) , in particular, K 2 ( Z [ C 3 × ( C 2 ) n ] ) is proven to be a finite abelian 2-group. As an application, we prove K 2 ( Z [ C 3 × ( C 2 ) 2 ] ) is an elementary abelian 2-group of rank at least 14, at most 16.