Presenting GL_n(k )

We give some extensions of known results concerning the finite presentability of the general linear group GL_n(R), the Steinberg group St_n(R) and the elementary group E_n(R), for suitable rings R. We obtain, in particular, a complete answer as to when GL_n(k ) is finitely presentable, where k is a field and k is the free associative k-algebra on the set T. Our first theorem extends the result of Behr [1] that SL_3(k[t]) is not finitely presentable if k is a field