The mod 2 cohomology of the linear groups over the ring of integers

Abstract

The Hopf algebra structure of the mod 2 cohomology of thegeneral linear group over the integers as a module over theSteenrod algebra was first computed by S. A. Mitchell [Math. Z.209 (1992), no. 2, 205 222; MR\Cite{Mitchell92:plus:205--222}[93b:55021]]. The main results ofthis paper involve determining the Hopf algebra structure of themod 2 cohomology of the general linear group, the special lineargroup and the Steinberg group (over the integers) as a moduleover the Steenrod algebra. An explicit description of thegenerators of the mod 2 cohomology is given