Intereting Posts

Number of subsets of $\{1,2, \ldots, n\}$ containing no three consecutive integers: recurrence equation?
Is it possible to elementarily parametrize a circle without using trigonometric functions?
Question about Feller's book on the Central Limit Theorem
Lemma about the integral of a function with compact support
How to solve this integral: $\int_0^\infty x^a e^{-bx}dx$?
Combinations of multisets – the theory?
Monkey typing ABRACADABRA and gamblers
Need a proofreading why all the units are satisfied $a^2-2b^2 =\pm1$ for $\mathbf{Z}$
The distance function is continuous.
Expanded form of Divided differences
Is a strictly Increasing, midpoint convex, symmetric probability function, iff it is midpoint concave/linear?
Differentiable function in the normed space $\,\mathcal{C}$
How to prove that $\omega (n) = O\Big{(} \frac{\log(n)}{\log(\log(n))}\Big{)}$ as $n \to \infty$?
Number of Relatively Prime Factors
For $M\otimes_R N$, why is it so imperative that $M$ be a right $R$-module and $N$ a left $R$-module?

What are the finite subgroups of $GL_2(\mathbb{Z})$?

I would quite like to know what the matrices which generate the subgroups are.

I know that this group has an index two subgroup which is isomorphic to $\langle x, y; x^6, y^4, x^3=y^2\rangle$ but

- Transitive subgroup of symmetric group
- computing the orbits for a group action
- Proof that the Rubik’s Cube group is 2-generated
- The group $E(\mathbb{F}_p)$ has exactly $p+1$ elements
- For finite abelian groups, show that $G \times G \cong H \times H$ implies $G \cong H$
- How to describe the Galois group of the compositum of all quadratic extensions of Q?

- a) I cannot remember facts about free products with amalgamation for more than $5$ minutes
- b) I do not know which matrix the $x$-generator corresponds to (or, I suppose, the $y$-generator, but I can easily find elements of order $4$…$6$ is more elusive).

**Note:** I have edited this answer as I got mixed up with $SL$ and $GL$ for some reason…

- Is there a geometric realization of Quaternion group?
- Question about permutation cycles
- Questions on Symmetric group of degree 5
- Problem on abelian group
- Subgroups of Prime Power Index
- For which cases with $2$ or $3$ prime factors do formulas for $gnu(n)$ exist?
- The use of conjugacy class and centralizer?
- Noncyclic Abelian Group of order 51
- Poincaré's theorem about groups
- Prove that every subgroup of an abelian group is a normal subgroup.

From *Trees* by Serre (chapter 3, section 4.3, corollary of theorem 8):

Theorem:Let $G$ be an amalgam $G_1 \underset{A}{\ast} G_2$ of two groups. Every finite subgroup of $G$ is contained in a conjugate of $G_1$ or $G_2$.

- If the infinite cardinals aleph-null, aleph-two, etc. continue indefinitely, is there any meaning in the idea of aleph-aleph-null?
- Is there any geometric way to characterize $e$?
- Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$
- How to apply Gaussian kernel to smooth density of points on 2D (algorithmically)
- Does the principle of mathematical induction extend to higher cardinalities?
- Interesting piece of math for high school students?
- rational functions on projective n space
- How find this inequality with $x_{1}+x_{2}+\cdots+x_{n}=1$
- Unbounded measurable set with different inner and outer measures
- Find the sum of $-1^2-2^2+3^2+4^2-5^2-6^2+\cdots$
- Math Behind Creating a “Perfect” Star
- Prove that $f$ has derivatives of all orders at $x=0$, and that $f^{(n)}(0)=0$ for $n=1,2,3\ldots$
- Prove that:$\sum_{i=1}^n\frac{1}{x_i}-\sum_{i<j}\frac{1}{x_i+x_j}+\sum_{i<j<k}\frac{1}{x_i+x_j+x_k}-\cdots+(-1)^{n-1}\frac{1}{x_1+\ldots+x_n}>0.$?
- When quotient map is open?
- Is there a way to find all roots of a polynomial equation?