### An elementary invariant problem and general linear group cohomology restricted to the diagonal subgroup, by Marian F. Anton

Conjecturally, for p an odd prime and R a certain ring of p-integers, the stable
general linear group GL(R) and the etale model for its classifying space have
isomorphic mod p cohomology rings. In particular, these two cohomology rings
should have the same image with respect to the restriction map to the diagonal
subgroup. We show that a strong unstable version of this last property holds for
any rank if p is regular and certain homology classes for SL(2,R) vanish.

Marian F. Anton <Marian.Anton@imar.ro>