J Austral Math Soc Ser A 59 pp353--365, 1995.

Commutators in Pseudo-Orthogonal Groups

F. A. Arlinghaus, L. N. Vaserstein and Hong You

Abstract

We study commutators in pseudo-orthogonal groups O_2nR (including unitary, sympletic and ordinary orthogonal groups) and in the conformal pseudo-orthogonal groups GO_2nR. We estimate the number of commutators, c(O_2nR) and c(GO_2nR), needed to represent every element in the commutator subgroup. We show that c(O_2nR) £ 4 if R satisfies the L-stable condition and either n ³ 3 or n = 2 and 1 is the sum of two units in R, and that c(GO_2nR) £ 3 when the involution is trivial and L = R^e. We also show that c(O_2nR) £ 3 and c(GO_2nR) £ 2 for the ordinary orthogonal group O_2nR over a commutative ring R of absolute stable rank 1 where either n ³ 3 or n = 2 and 1 is the sum of two units in R.

1991 AMS Subject Classification: 20G35, 20H25

Browse the article

Authors

F. A. Arlinghaus

Department of Mathematics, Youngstown State University, Youngstown, Ohio 44455, USA.

L. N. Vaserstein

Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.

mailto:vstein@math.psu.edu

Hong You

Department of Mathematics, Northeast Normal University, Changchun 130024, People's Republic of China.