Algebraic K-theory of special groups

Following the introduction of an algebraic K-theory of special groups in [Dickmann and Miraglia, Algebra Colloq. 10 (2003) 149–176], generalizing Milnor's mod 2 K-theory for fields, the aim of this paper is to compute the K-theory of Boolean algebras, inductive limits, finite products, extensions, SG-sums and (finitely) filtered Boolean powers of special groups. A parallel theme is the preservation by these constructions of property [SMC], an analog for the K  -theory of special groups of the property “multiplication by l(-1)l(-1) is injective” in Milnor's mod 2 K-theory (see [Milnor, Invent. Math. 9 (1970) 318–344]).