## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 353-365 |

Number of pages | 13 |

Journal | Journal of the Australian Mathematical Society |

Volume | 59 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1995 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)