The Yagita invariant of general linear groups

Abstract

We give a definition of the Yagita invariant at a prime p of an arbitrary group G, and compute the invariant for each prime for the general linear groups over any integrally closed subring of the complex numbers. We also compute the invariants for special linear groups over the same rings, except in some cases when both the degree of the linear group and the ring are `small' compared to p.