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

Abstract

For an odd quadratic space V of Witt index ě 3 over a commutative ring with pseudoinvolution, we classify the subgroups of the odd unitary group UpVq that are normalized by the elementary subgroup EU pe 1 ,e´1q pVq defined by a hyperbolic pair pe1, e´1q in V. Further we correct some minor mistakes that exist in the literature on odd unitary groups.2010 Mathematics Subject Classification. 20G35, 20H25.

Visualization for Petrov's Odd Unitary Group

“…Later A. Bak and R. Preusser [7] studied a subclass of Petrov's odd unitary groups which contain all the classical Chevalley groups, and classified the E-normal subgroups of the members of this subclass. The E-normal subgroups of odd unitary groups are also studied by W. Yu, Y. Li and H. Liu in [8] and also by R. Preusser in [9].…”