Products of Quasi-Involutions in Unitary Groups

Abstract

Given a regular –-hermitian form on an n-dimensional vector space V over a commutative field K of characteristic ≠ 2 ( $$n \in \mathbb{N} $$ ). Call an element σ of the unitary group a quasi-involution if σ is a product of commuting quasi-symmetries (a quasi-symmetry is a unitary transformation with a regular (n−1)-dimensional fixed space). In the special case of an orthogonal group every quasi-involution is an involution. Result: every unitary element is a product of five quasi-involutions. If K is algebraically closed then three quasi-involutions suffice.