The Yagita invariant of general linear groups

TL;DR

This paper defines the Yagita invariant for any group and computes it for general and special linear groups over integrally closed subrings of complex numbers, revealing new algebraic insights.

Contribution

It introduces a general definition of the Yagita invariant and provides explicit computations for linear groups over various rings, extending prior knowledge.

Findings

Computed Yagita invariants for general linear groups over complex subrings

Computed invariants for special linear groups with some exceptions

Extended understanding of group invariants in algebraic settings

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.