The vanishing of SK1 can be interpreted as saying that K1 is generated by the image of GL1 in GL. When this fails, one can ask whether K1 is generated by the image of GL2. For a Dedekind domain, this is the case: indeed, K1 is generated by the images of GL1 and SL2 in GL. The subgroup of SK1 generated by SL2 may be studied by Mennicke symbols. For Dedekind domains with all quotients by maximal ideals finite, SK1 is a torsion group.