The orthogonal group over a local ring is \(4\)-reflectional (Q1326548)
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scientific article; zbMATH DE number 569274
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The orthogonal group over a local ring is \(4\)-reflectional |
scientific article; zbMATH DE number 569274 |
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The orthogonal group over a local ring is \(4\)-reflectional (English)
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21 November 1994
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Let \(R\) be a commutative local ring such that 2 is a unit in \(R\). The author shows that every element in the orthogonal group of a free \(R\)- module of finite rank is a product of two involutions in that group. For a cyclic isometry the involutions are constructed directly. This, combined with the bireflectionality of an orthogonal group for a vector space, produces the desired result.
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product of involutions
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commutative local ring
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orthogonal group
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free \(R\)-module of finite rank
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cyclic isometry
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bireflectionality
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