Intereting Posts

Number of solutions to $x+y+z = n$
Is π equal to 180$^\circ$?
Is there a prime number between every prime and its square?
Describing Functions on a Manifold
Infinite Series $\left(\frac12+\frac14-\frac23\right)+\left(\frac15+\frac17-\frac26\right)+\left(\frac18+\frac{1}{10}-\frac29\right)+\cdots$
The sum of a polynomial over a boolean affine subcube
Confusion with Euler-Lagrange Derivation
Is $\mathbb{Q}=\{a+bα+cα^2 :a,b,c ∈ \mathbb{Q}\}$ with $α=\sqrt{2}$ a field?
On $GL_2(\mathbb F_3)$
If $ab=ba$, Prove $a^2$ commutes with $b^2$
Field and Algebra
If a subring of a ring R has identity, does R also have the identity?
Map from binary sequences on $\{0,1\}$ into the Cantor set $C$ respects order
Partial derivative VS total derivative?
How was the determinant of matrices generalized for matrices bigger than $2 \times 2$?

I have the dicyclic group $G$ of order 12 generated by $x,y$ satisfying $x^4 = y^3 = 1$ and $xyx^{-1} = y^2$, and am trying to determine whether the symmetric group $S_6$ contains a subgroup isomorphic to it.

So far I’ve tried looking for an appropriate set of 6 elements for $G$ to act on, and hoping that the permutation representation $ \phi: G \to S_6$ is injective, but haven’t had any luck: $ \phi$ is not injective for the action of $G$ conjugating its set of 6 elements of order 4, nor is it injective for the action of $G$ translating its set of 6 cosets of a subgroup of order 2.

Is it even true that $S_6$ does contain such a subgroup isomorphic to $G$, and if so how would I construct the isomorphism?

- Is the ideal generated by an irreducible polynomial prime?
- Why do we have to do the same things to both sides of an equation?
- Is this an isomorphism possible?
- Notation for n-ary exponentiation
- Prove that $H$ is a abelian subgroup of odd order
- A problem with tensor products

- Prove that a non-abelian group of order $pq$ ($p<q$) has a nonnormal subgroup of index $q$
- Determining whether ${p^{n-2} \choose k}$ is divisible by $p^{n-k -2}$ for $1 \le k < n$
- $R$ is a commutative integral ring, $R$ is a principal ideal domain imply $R$ is a field
- $H$ is a maximal normal subgroup of $G$ if and only if $G/H$ is simple.
- The smallest symmetric group $S_m$ into which a given dihedral group $D_{2n}$ embeds
- Finitely generated module with a submodule that is not finitely generated
- Show that $\mathbb{Q}^+/\mathbb{Z}^+$ cannot be decomposed into the direct sum of cyclic groups.
- Norm of powers of a maximal ideal (in residually finite rings)
- How to prove $e^{A \oplus B} = e^A \otimes e^B$ where $A$ and $B$ are matrices? (Kronecker operations)
- $1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent

If $y$ is of order $3$, it must have cycle type $(abc)$ or $(abc)(def)$. If $x$ is of order $4$, it must have cycle type $(abcd)$ or $(abcd)(ef)$. Also, you know how $x$ acts on $y$ by conjugation…

- Evaluate $\cot^2\left(\frac{1\pi}{13}\right)+\cot^2\left(\frac{2\pi}{13}\right)+\cdots+\cot^2\left(\frac{6\pi}{13}\right)$
- Why is the prime spectrum of a domain irreducible in the Zariski topology
- Help finding this set
- Ramanujan log-trigonometric integrals
- Is this question of sequence a Mathematical one, i.e. does it have objectively only one answer for each subpart.
- Solving equations of form $3^n – 1 \bmod{k} = 0$, $k$ prime
- Prove that $\dfrac{|x+y|}{1+|x+y|}\leq\dfrac{|x|}{1+|x|}+\dfrac{|y|}{1+|y|}$ for any $x,y$
- Reasoning that $ \sin2x=2 \sin x \cos x$
- A couple of formulas for $\pi$
- Proof that $\lim_{n\rightarrow \infty} \sqrt{n}=1$
- Rate of convergence in the central limit theorem (Lindeberg–Lévy)
- Mathematical symbol for “and”
- Reason behind standard names of coefficients in long Weierstrass equation
- What is the set-theoretic definition of a function?
- Why does a minimal prime ideal consist of zerodivisors?