### Abstract

There are several subgroups of the Elementary group E(B, I) and of the Steinberg group St(B, I) which lie at the congruence level I^{2}. We describe their interrelationships and give examples to show that they can be distinct. Our main result is that, although the group E(B, I) depends on the choice of the ambient ring B, its commutator subgroup does not. In fact, the commutator subgroup is the intersection of Gl(I^{2}) with E(Z⊕I, I).

Original language | English (US) |
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Pages (from-to) | 123-132 |

Number of pages | 10 |

Journal | Journal of Pure and Applied Algebra |

Volume | 35 |

Issue number | C |

DOIs | |

State | Published - Jan 1 1985 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Keywords

- Elementary group
- algebraic K-theory
- congruence level subgroup
- relative Steinberg groups

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## Cite this

Geller, S. C., & Weibel, C. (1985). Subgroups of the elementary and Steinberg groups of congruence level I

^{2}.*Journal of Pure and Applied Algebra*,*35*(C), 123-132. https://doi.org/10.1016/0022-4049(85)90035-0