The defining short exact sequence for Milnor's $K_2(R)$ ($R$ any ring) is

$$0\rightarrow K_2(R)\rightarrow St(R)\rightarrow E(R)\rightarrow 0$$

where $St(R)$ and $E(R)$ are the Steinberg and elementary groups. If we cheat a little on the definition of "short" this extends to

$$0\rightarrow K_2(R)\rightarrow St(R)\rightarrow GL(R)\rightarrow K_1(R)\rightarrow 0$$