93i:20060 20J06 20G40

Mislin, Guido ^{(}CH-ETHZ^{)}

On the cohomology of finite groups of Lie type. Illinois J. Math. 36 (1992), no. 2, 275–285. Let F_{q} denote the finite field of q elements, and let G be a connected reductive group scheme over spec(F_{q}). This paper is concerned with the cohomology of the finite groups G(F_{q^{n}}) of F_{q^{n}}-rational points of G with coefficients in Z/l, where l is a prime different from p = char(F_{q}). (These groups G(F_{q^{n}}) and their central quotient include all the finite groups of Lie type.) The main result states that the inclusion G(F_{q}) → G(F_{q^{n}}) induces an H^{∗}( ; Z/l)-isomorphism if and only if G(F_{q}) and G(F_{q^{n}}) have isomorphic Sylow l-subgroups.

Martin W. Liebeck (4-LNDIC)

\begin{matrix}c \\ ◯ \end{matrix} Copyright American Mathematical Society 1993, 1996