Intereting Posts

Order of nontrivial elements is 2 implies Abelian group
compute one improper integral involving arctangent
How do we use derivatives in our daily lives
Which of the following is not true?
Can two integer polynomials touch in an irrational point?
Computing $ \int_a^b \frac{x^p}{\sqrt{(x-a)(b-x)}} \mathrm dx$
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
Normality is not hereditary
Odd and even numbers in Pascal's triangle-Sierpinski's triangle
What is the importance of Calculus in today's Mathematics?
Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$
How does one prove that the spectral norm is less than or equal to the Frobenius norm?
Theorem 6.15 in Baby Rudin: If $a<s<b$, $f$ is bounded on $$, $f$ is continuous at $s$, and $\alpha(x)=I(x-s)$, then . . .
Proving the irrationality of $\sqrt{5}$: if $5$ divides $x^2$, then $5$ divides $x$
Proof of rank-nullity via the first isomorphism theorem

Is there a non trivial homomorphism $f: SU(2) \to O(2)$? Is there a concrete description of $Hom(SU(2), O(2))$?

- Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
- UFDs are integrally closed
- The product of all the elements of a finite abelian group
- Tips for writing proofs
- An equation of form $x^{2}+ax+b=0$ might have infinite amount of solutions in a ring $(R,+,\cdot)$
- Abstract algebra: for a polynomial $p$, prove $\sigma(\tau(p))=(\sigma\tau)(p)$ for all $\sigma, \tau \in S_n$
- Centre of symmetric group algebra
- Show that a nonabelian group must have at least five distinct elements
- Free and proper action
- Tensor product of two finitely-generated modules over a local ring is zero

No. $\text{ker}(f)$ is a normal subgroup of $SU(2)$. Since $SU(2)$ is a simple Lie group, its normal subgroups are either trivial subgroup or its center or itself. So $\text{im}(f)=SU(2)$ or $SU(2)/\{\pm I\}$, or the trivial group. Among them only the trivial group is a subgroup of $O(2)$.

- Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
- Obtaining Wirtinger presentation using van Kampen theorem
- Polygon and Pigeon Hole Principle Question
- Prove that the difference between two rational numbers is rational
- Prove $\langle \mathbb{N}, x \mapsto x +1, 1 \rangle$ is a Peano system without circular reasoning
- Space of eigenvectors
- How do I calculate the right value of this Integral?
- Proving the length of angle bisector
- Invertibility of the Product of Two Matrices
- Modern formula for calculating Riemann Zeta Function
- Categorial definition of subsets
- Calculus 2 integral $\int {\frac{2}{x\sqrt{x+1}}}\, dx$
- Count the number of paths from $(0,0)$ to $(2n,n)$ than never go above $y=x$
- Show that $\int_{\pi}^{\infty} \frac{1}{x^2 (\sin^2 x)^{1/3}} dx$ is finite.
- Taking away infinitely many elements infinitely many times