Unitary subgroup of the Sylow 2-subgroup of the group of normalized units in an infinite commutatuve group ring

摘要

Let G be an abelian group, K a commutative ring with unity of prime characteristic p and let V (KG) denote the group of normalized units of the group ring KG . An element u= g∈G α g g ∈V (KG) is called unitary if u .1 coincides with the element u . = g∈G α g g .1 . The set of all unitary elements of the group V (KG) forms a subgroup V . (KG) . S. P. Novikov had raised the problem of determining the invariants of the group V . (KG) when G has a p -power order and K is a finite field of characteristic p . This problem was solved by A. Bovdi and the author. We gave the Ulm–Kaplansky invariants of the unitary subgroup of the Sylow p -subgroup of V (KG) whenever G is an arbitrary abelian group and K is a commutative ring with unity of odd prime characteristic p without nilpotent elements. Here we continue this works describing the unitary subgroup of the Sylow 2-subgroup of the group V (KG) in case when G is an arbitrary abelian group and K is a commutative ring with unity of characteristic 2 without zero divisors.