The Rost invariant has zero kernel for quasi-split trialitarian groups

TL;DR

This paper provides detailed proof that the kernel of the Rost invariant is zero for quasi-split trialitarian groups, complementing existing literature with mechanical details for clarity.

Contribution

It supplies the missing detailed proof for the zero kernel of the Rost invariant in the context of quasi-split trialitarian groups, enhancing understanding of this mathematical property.

Findings

Kernel of the Rost invariant is zero for quasi-split trialitarian groups

Complements existing proofs with detailed mechanical steps

Supports the results discussed in The Book of Involutions

Abstract

The Book of Involutions includes the NON-trivial parts of a proof that the kernel of the Rost invariant is zero for quasi-split trialitarian groups. We record the missing (mechanical) details here. This note is recorded here on the arxiv only for the convenience of readers who like the style of The Book and obviously does not merit publication. A proof in Harder's style can be found in a paper by Chernousov (see the bibliography).