Prestability for quadratic K1 of Λ-1-fold stable rings

The general quadratic group U2n and its elementary subgroup EU2n are analogs in the theory of the general linear group GLn and its elementary subgroup En. It is known, for GLn, K1=GL1/〈(a+c+abc)−1(a+c+cba)|a+c+abc∈GL1〉 under the first Bass stable range condition on the ring of entries. In this article we give a description for KU1 under the Λ-1-fold stable range condition on the ring of entries.