A note on Quadratic and Hermitian Groups

TL;DR

This paper extends the understanding of quadratic and hermitian groups by establishing a local-global principle and analyzing the nilpotent structure of their unstable K_1-groups, generalizing previous results.

Contribution

It introduces an analogue of Quillen's Local-Global Principle for elementary subgroups of quadratic and hermitian groups, and shows their unstable K_1-groups are nilpotent-by-abelian.

Findings

Established a local-global principle for quadratic and hermitian groups.

Proved that unstable K_1-groups of hermitian groups are nilpotent-by-abelian.

Generalized earlier results by Bak, Hazrat, and Vavilov.

Abstract

In this article we deduce an analogue of Quillen's Local-Global Principle for the elementary subgroup of the general quadratic group and the hermitian group. We show that the unstable K_1-groups of the hermitian groups are nilpotent by abelian. This generalizes earlier results of A. Bak, R. Hazrat, N. Vavilov and etal..