TY - JOUR

T1 - Commutators in pseudo-orthogonal groups

AU - Arlinghaus, F. A.

AU - Vaserstein, L. N.

AU - You, Hong

PY - 1995/12

Y1 - 1995/12

N2 - We study commutators in pseudo-orthogonal groups O2n R (including unitary, symplectic, and ordinary orthogonal groups) and in the conformal pseudo-orthogonal groups GO2nR. We estimate the number of commutators, c(O2nR) and c(GO2nR), needed to represent every element in the commutator subgroup. We show that c(O2nR)≤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(GO2nR)≤3 when the involution is trivial and A = R ∊. We also show that c(O2nR)≤3 and c(GO2nR)≤ 2 for the ordinary orthogonal group O2n 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.

AB - We study commutators in pseudo-orthogonal groups O2n R (including unitary, symplectic, and ordinary orthogonal groups) and in the conformal pseudo-orthogonal groups GO2nR. We estimate the number of commutators, c(O2nR) and c(GO2nR), needed to represent every element in the commutator subgroup. We show that c(O2nR)≤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(GO2nR)≤3 when the involution is trivial and A = R ∊. We also show that c(O2nR)≤3 and c(GO2nR)≤ 2 for the ordinary orthogonal group O2n 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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U2 - 10.1017/S1446788700037253

DO - 10.1017/S1446788700037253

M3 - Article

AN - SCOPUS:84879206815

SN - 1446-7887

VL - 59

SP - 353

EP - 365

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 3

ER -