Normalizer of \(\Gamma_1(m)\) (Q5929395)
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scientific article; zbMATH DE number 1584994
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Normalizer of \(\Gamma_1(m)\) |
scientific article; zbMATH DE number 1584994 |
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Normalizer of \(\Gamma_1(m)\) (English)
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2 July 2001
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For \(m\in \mathbb{N}\) let \(\Gamma_1(m)\) be the congruence subgroup of the modular group \(\text{PSL} (2,\mathbb{Z})\) defined by \(\Gamma_1(m)= \{A: z\mapsto \frac{az+b} {cz+d}\in \text{PSL} (2,\mathbb{Z})\mid c\equiv 0\bmod m\}\). The normalizer of \(\Gamma_1(m)\) in \(\text{PSL} (2,\mathbb{R})\) is described using the Fricke involutions.
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congruence subgroup
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modular group \(\text{PSL} (2,\mathbb{Z})\)
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normalizer
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Fricke involutions
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