# Groups normalized by the odd unitary group

## TL;DR

This paper defines quadratic forms on bimodules and proves a classification theorem for subgroups of the general linear group normalized by the elementary unitary group, under certain conditions.

## Contribution

It introduces a new definition of quadratic forms on bimodules and establishes a sandwich classification theorem for specific subgroup structures.

## Key findings

- Classification theorem for subgroups normalized by elementary unitary groups
- Extension of quadratic form theory to bimodules
- Conditions for hyperbolic parts in bimodules

## Abstract

We will give a definition of quadratic forms on bimodules and prove the sandwich classification theorem for subgroups of the general linear group $\mathrm{GL}(P)$ normalized by the elementary unitary group $\mathrm{EU}(P)$ if $P$ is a nondegenerate bimodule with large enough hyperbolic part.