5:38 AM
The tag was created. Obviously a meta tag, I guess it can be safely removed.
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$123456789 \times x$= What can $x$ be to give an obvious answer? I have got $0,1,10,10^n$ for integer n, $\pi$ and all the above mltiply by $i$ will also be an obvious answer. Are there any other solutions? Any help/contribution appreciated. Note: $\pi$ works because you must give an exact an...

It seems that this is not the first time a tag with this name appeared on the site: data.stackexchange.com/math/query/787716/… and data.stackexchange.com/math/query/858309/…
Another new tag is . Created by janmarqz.
4

I read about how Hecke groups are a particular generalisation of the modular group, generalising one of the generators of the modular group to $z\mapsto z + \lambda$. Have people studied generalisations of the other generator of the modular group, perhaps generalising to $z \mapsto \dfrac{-1}{z^n... 4 I've been studying the hyperbolic plane and the action of the group$PSL(2,\mathbb{R})$on it. I found that the modular group$PSL(2,\mathbb{Z})$is a discrete subgroup of$PSL(2,\mathbb{R})$so it's Fuchsian.But where does the name of the Modular group come from?How is it related with the Moduli... 2 Definition: For a subgroup$G$of the group$PSL(2,\mathbb{C})$acting on$\mathbb{P}^1$, its domain of discontinuity is the set of all points,$z$, with the following properties:$1.$The stabilizer$G_z$of$z$is finite.$2.\exists U$, a neighbourhood of$z$such that,$\space \space\...

2

Does anyone know how to describe Möbius transformations with integer coefficients defined on the upper half plane in terms of $z+1$ and $1/z$? Some people call it the modular group. I would appreciate any suggestions. Thanks.

2

I'm probably in over my head, but I came across the following sentence in a thesis by Evan Oliver entitled "Congruence Subarrangements of the Schmidt Arrangement": "The modular group is the set of all matrices in P SL2(Z) whose elements reduce component-wise to the identity matrix over a prime i...

3

The modular group $PSL_2(\mathbb{Z})$ acts on the hyperbolic half-space $H$ by $$h\cdot z=\frac{az+b}{cz+d},\;z\in H,\;h=\begin{pmatrix}a&b\\c&d\end{pmatrix}\in PSL_2(\mathbb{Z})$$ with $ad-bc=1$. The modular group is generated by two elements $S$ and $T$ such that $$S^2=(ST)^3=1,$$ where we can ...

3

Let $\Gamma$ be a finite index subgroup of $\Gamma(1)=SL_2(\mathbf{Z})$ and $f$ a modular function for $\Gamma$. By this I mean a meromorphic function defined on the upper half-plane $f: \mathfrak{h} \to \mathbf{C}$, satisfying a growth condition at infinity, which is invariant by $\Gamma$: for e...

2

In the paper http://projecteuclid.org/download/pdf_1/euclid.ijm/1255632506 it is stated without proof that the commutator subgroup of the modular group is a free group of rank $2$. Can anyone give a reference for the proof of this fact?

3

This is a very small question. Let $\mathbb{\Gamma} = \mathrm{SL_2}(\mathbb{Z})$ be the modular group, $\mathcal{F} = \{z \in \mathbb{C} ;\; \lvert z \rvert \geq 1,\; \lvert \Re (z) \rvert \leq 1/2\}$ its fundamental domain. I (probably) don't understand the following argument made by Toshits...

In mathematics, the modular group is the projective special linear group PSL(2,Z) of 2 x 2 matrices with integer coefficients and unit determinant. The matrices A and -A are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation to moduli spaces and not from modular arithmetic. == Definition == The modular group Γ is the group of linear fractional transformations of the upper half of the complex plane which have the form z ↦ ...
And there is also . The tag creator (Hector Blandin) also created the tag-excerpt.
2

Let $\mathbb{K}$ be a field and $A$ a finite dimensional $\mathbb{k}$-algebra with identity $1_{A}$. For two $A$-modules $M$ and $N$ we have the set of all $A$-linear maps from $M$ to $N$ denoted $\mathrm{Hom}_{A}(M,N)$. This set is not in general an $A$-module neither by the left nor by the righ...

9 hours later…
3:10 PM
@MartinSleziak And the tag is back. (Created by onurcanbektas.)
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In the book of Analysis On Manifolds by Munkres, at page 141, it is given that However, I think there is a problem in the existence such an $M$. Reason: Because we do know that the supports of $\phi_i$s, i.e $S_i$s, will form a cover for $A$, and hence for $D$, but by the compactness of $D$,...

3 hours later…
5:50 PM
Jun 28 at 11:32, by Martin Sleziak
The tag was created about a yera ago: https://chat.stackexchange.com/transcript/3740/2017/7/18 It seems that it is used for all sorts of stuff.

6:03 PM
@MichaelHardy Since you are the tag-creator, I thought it could be useful to let you know that I have opened a thread on meta about this tag: What is the (calculus-identities) tag intended for?Martin Sleziak 16 secs ago

1

The tag calculus-identities has been created about a year ago in this question: Quotient rule/Quotient rule. When I look at questions which have this tag now or which were tagged with this tag in the past, it seems that people are using it for all sorts of stuff. (Basically anything where some ...