# A note on general quadratic groups

## TL;DR

This paper extends the local-global principle to transvection subgroups of general quadratic groups and revisits stabilization results for their K_1-functor, advancing algebraic K-theory understanding.

## Contribution

It introduces an analogue of Quillen--Suslin's principle for quadratic groups and re-examines stabilization results in this context.

## Key findings

- Established a local-global principle for transvection subgroups
- Revisited and extended stabilization results for K_1-functor
- Provided new insights into algebraic K-theory of quadratic groups

## Abstract

We deduce an analogue of Quillen--Suslin's local-global principle for the transvection subgroups of the general quadratic (Bak's unitary) groups. As an application we revisit the result of Bak--Petrov--Tang on injective stabilization for the K_1-functor of the general quadratic groups.