UNRAMIFIED BRAUER GROUPS OF FINITE SIMPLE GROUPS OF LIE TYPE Al.

We study the subgroup B₀(G) of H²(G,Q/Z) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B₀(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B₀(G) is trivial for finite simple groups of lie type A_e. [ABSTRACT FROM AUTHOR]