Arlinghaus, F. A.; Vaserstein, L. N.; You, Hong Commutators in pseudo-orthogonal groups. (English) Zbl 0847.20042 J. Aust. Math. Soc., Ser. A 59, No. 3, 353-365 (1995). Given a pseudo-orthogonal group \(G=\mathrm{O}_{2n}R\) or \(G=\mathrm{GO}_{2n}R\) (this includes unitary, symplectic, orthogonal groups), the authors try to estimate the number \(c(G)\) which by definition is such that any product of commutators in \(G\) is also the product of at most \(c(G)\) commutators. They succeed for semi-local rings \(R\) and for rings satisfying a stable range condition that make the ring behave like a semi-local ring. There are several cases and the estimates vary from two to four. As expected, the proofs use clever matrix manipulations. Reviewer: Wilberd van der Kallen (Utrecht) Cited in 2 Documents MSC: 20G35 Linear algebraic groups over adèles and other rings and schemes 20F12 Commutator calculus 20F05 Generators, relations, and presentations of groups 20H25 Other matrix groups over rings Keywords:pseudo-orthogonal groups; orthogonal groups; products of commutators; semi-local rings; stable range conditions PDFBibTeX XMLCite \textit{F. A. Arlinghaus} et al., J. Aust. Math. Soc., Ser. A 59, No. 3, 353--365 (1995; Zbl 0847.20042)