We study commutators in pseudo-orthogonal groups O 2n R (including unitary, symplectic, and ordinary orthogonal groups) and in the conformal pseudo-orthogonal groups GO^R. We estimate the number of commutators, c(C>2nR) and c(G02 n R), needed to represent every element in the commutator subgroup. We show that c(O 2n R) < 4 if R satisfies the A-stable condition and either n > 3 or n = 2 and 1 is the sum of two units in R, and that c(GO 2n R) < 3 when the involution is trivial and A = R f . We also show that ciO^R) < 3 and c(GO 2n R) < 2 for the ordinary orthogonal group O 2rl R over a commutative ring R of absolute stable rank 1 where either n > 3 or n = 2 and 1 is the sum of two units in R.

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We describe subgroups of CL2A which are normalized by elementary matrices for rings A satisfying the first stable range condition, Banach algebras A, ven Neumann regular rings A, and other rings A .

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