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 -