The E-normal structure of Petrov's odd unitary groups over commutative rings

TL;DR

This paper classifies certain subgroups of odd unitary groups over commutative rings with pseudoinvolution, focusing on those normalized by elementary subgroups, and corrects existing literature errors.

Contribution

It provides a classification of subgroups normalized by elementary groups in odd unitary groups over rings, and rectifies previous inaccuracies in the literature.

Findings

Classified subgroups normalized by elementary groups in odd unitary groups.

Corrected minor errors in existing literature on odd unitary groups.

Extended understanding of the structure of odd unitary groups over rings.

Abstract

For an odd quadratic space $V$ of Witt index $\geq 3$ over a commutative ring with pseudoinvolution, we classify the subgroups of the odd unitary group $U(V)$ that are normalized by the elementary subgroup $EU_{(e_1,e_{-1})}(V)$ defined by a hyperbolic pair $(e_1,e_{-1})$ in $V$. Further we correct some minor mistakes that exist in the literature on odd unitary groups.