Cohomological behaviour of the reduction modulo a prime of \(GL_ 3(Z)\) (Q798440)

Let p be a prime. Generators and relations for the cohomology ring of GL(3,Z/p) [resp. GL(3,Z)] with integral coefficients were given by \textit{D. Quillen} [Ann. Math., II. Ser. 96, 552-586 (1972; Zbl 0249.18022)] and \textit{M. Tezuka} and \textit{N. Yagita} [J. Algebra 81, 295-303 (1983; Zbl 0519.18013)] (resp. by \textit{C. Soulé} [Topology 17, 1-22 (1978; Zbl 0382.57026)]). Now let \(r:GL(3,Z)\to GL(3,Z/p)\) be reduction mod p and \(r^*\) the induced map on cohomology. This paper describes \(r^*\) explicitly in terms of the generators mentioned above. The proofs are mostly given in detail.