# Fungrim entry: 094772

Symbol: SL2Z $\operatorname{SL}_2(\mathbb{Z})$ Modular group
Whether $\operatorname{SL}_2(\mathbb{Z})$ or $\operatorname{PSL}_2(\mathbb{Z})$ should be called "the modular group" is an arbitrary convention. Here we allow any element of $\operatorname{SL}_2(\mathbb{Z})$ to represent an element of the modular group, but we use $\operatorname{PSL}_2(\mathbb{Z})$ when uniqueness is desired.
Definitions:
Fungrim symbol Notation Short description
SL2Z$\operatorname{SL}_2(\mathbb{Z})$ Modular group
PSL2Z$\operatorname{PSL}_2(\mathbb{Z})$ Modular group (canonical representatives)
Source code for this entry:
Entry(ID("094772"),
SymbolDefinition(SL2Z, SL2Z, "Modular group"),
Description("Whether", SL2Z, "or", PSL2Z, "should be called \"the modular group\" is an arbitrary convention. Here we allow any element of", SL2Z, "to represent an element of the modular group, but we use", PSL2Z, "when uniqueness is desired."))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC