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Marcos
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6 votes
1 answer
126 views

Prove that $\lim_{n\to\infty}\|f_n-f\|_p=\lim_{n\to\infty}\|g_n-g\|_p=0$

6 votes
0 answers
276 views

Proof of a weighted norm inequality.

6 votes
1 answer
132 views

$(\int_{\mathbb{R}}|\int_\mathbb{R}{\mathcal{F}^{-1}}(\chi_{(t,\infty)}\hat{f})(\xi)m'(t)dt|^pd\xi)^{1/p}\leq C_p\|m'\|_{L^1}\|f\|_{L^p}$

5 votes
0 answers
79 views

There are uncountably many subgroups of $\text{Gal}( \bar{\mathbb{Q}}/\mathbb{Q})$ of index $2$.

5 votes
1 answer
104 views

Find the presentation for the kernel of a map from $G=\langle a,b,c\mid aba=bab,bc=cb\rangle$ to $\mathbb{Z}$.

5 votes
1 answer
50 views

If $G\to\mathbb{Z}$ and $H\to\mathbb{Z}$ are surjective homomorphisms prove that exists $G\times H\to\mathbb{Z}$ with finitely generated kernel.

5 votes
1 answer
177 views

Union of powers of a well-ordered set is well-ordered.

5 votes
1 answer
258 views

Let $G$ be a finite group, $H$, $K$ be normal subgroups and $P$ a sylow p-subgroup . Then $PH \cap PK=P\left( H\cap K\right)$.

5 votes
1 answer
157 views

Group of an Elliptic curve.

5 votes
2 answers
427 views

Number of points of an elliptic curve

4 votes
1 answer
118 views

Dimension of $R\left/aR\right.$.

4 votes
1 answer
322 views

Every ring $R$ has a minimal prime ideal.

4 votes
1 answer
85 views

Let $A$ be abelian of order $m^2$ with $|A[d]|=d^2$ for every $d\mid m$. Prove $A\cong \Bbb{Z}/m\Bbb{Z}\times\Bbb{Z}/m\Bbb{Z}$

3 votes
0 answers
426 views

An exact sequence involving the Picard group.

3 votes
2 answers
101 views

Completion of $\mathbb{F}_2[x]$

3 votes
1 answer
729 views

Set of singular points of a normal variety.

3 votes
1 answer
251 views

Riemann-Hurwitz proof from Lang's Introdution to Algebraic and Abelian Functions

3 votes
1 answer
70 views

Compute $\dim_{\mathbb{Q}}(\mathbb{Q}[s^{\pm 1},t^{\pm 1}]/(t^2-t+1,s^2t-st+s-1))$

3 votes
0 answers
139 views

Fermat curve in Weierstrass form.

2 votes
1 answer
165 views

Lift roots of a polynomial from $\mathbb{F}_p$ to $\mathbb{Q}_p$

2 votes
1 answer
53 views

If $E/\mathbb{Q}$ is an elliptic curve and $j(E)=0$ then $y^2=x^3+D$ for some $6$-th power free integer $D$.

2 votes
0 answers
107 views

Equivalent definition of Sobolev space.

2 votes
1 answer
67 views

Roots of $x^4+x^3+x^2+x+1$ over $\mathbb{Z}_3[x]/(x^3-x+1)$.

2 votes
1 answer
37 views

Number of ways of take $m$ numbers from $\lbrace 1,\dots,n\rbrace$ such that the subsequences are of length $2^k-1$ for some $k$.

2 votes
1 answer
60 views

The set of irrational characters is dense in $\text{Hom}(G,\mathbb{R})$ for finitely generated $G$.

2 votes
0 answers
57 views

Find all natural numbers $n$ such that $\binom{n+1}{k}$ is even $\forall~k=1,\dots,n$.

2 votes
0 answers
95 views

$F_2\ltimes F_2^{2n-4}$ is a subgroup of $\mathrm{Aut}(F_n)$.

2 votes
1 answer
66 views

Kernel of group homomorphism $G\times G\to\mathbb{Z}$.

2 votes
1 answer
93 views

$\mathbb{Z}\rtimes\mathbb{Z}$ is left-orderable but not right-orderable.

2 votes
2 answers
225 views

Prove that a map beween manifolds that is smooth when composed by an embedding is smooth.