Structure of Hyperbolic Unitary Groups II: Classification of E-normal Subgroups

TL;DR

This paper classifies certain subgroups of hyperbolic unitary groups that are normalized by elementary subgroups, extending the understanding of their structure under specific algebraic conditions.

Contribution

It proves the sandwich classification conjecture for subgroups normalized by elementary groups in hyperbolic unitary groups over quasi-finite rings.

Findings

Established the classification for normalized subgroups in the specified setting.

Extended the theory to quasi-finite rings with involution.

Provided a framework for understanding subgroup structures in hyperbolic unitary groups.

Abstract

This paper proves the sandwich classification conjecture for subgroups of an even dimensional hyperbolic unitary group $U_{2n}(R,\Lambda)$ which are normalized by the elementary subgroup $EU_{2n}(R,\Lambda)$, under the condition that $R$ is a quasi-finite ring with involution, i.e a direct limit of module finite rings with involution, and $n\geq 3$.