Abstract

We say that a group is anti-solvable if all of its composition factors are non-abelian. We consider a particular family of anti-solvable finite groups containing the simple alternating groups for n 66 and all 26 sporadic simple groups. We prove that, if K is a perfect field and X is a homogeneous space of a smooth algebraic K-group G with finite geometric stabilizers lying in this family, then X is dominated by a G-torsor. In particular, if G SLn, all such homogeneous spaces have rational points.