Stabilizers of edges in general linear groups acting on trees (Q2705014)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stabilizers of edges in general linear groups acting on trees |
scientific article |
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Stabilizers of edges in general linear groups acting on trees (English)
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15 May 2001
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general linear groups
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actions on trees
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stabilizers of edges
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Bruhat-Tits buildings
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centres
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amalgamated free products
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The group \(G=\text{GL}_2(A)\), \(A=k[t]\) the polynomial ring over the field \(k\), acts on a tree, its Bruhat-Tits building. If \(k\) is perfect or the characteristic of \(k\) is not 2, then \(T\) has an edge whose stabilizer in \(G\) is the centre \(Z(G)\) of \(G\). Hence, \(G\) splits as a non-trivial amalgamated free product over its centre.
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