Robert Cardona's user avatar
Robert Cardona's user avatar
Robert Cardona's user avatar
Robert Cardona
  • Member for 12 years
  • Last seen more than 2 years ago
  • Barcelona, Spain
23 votes
3 answers
7k views

Show group of order $4n + 2$ has a subgroup of index 2.

20 votes
2 answers
3k views

Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$

13 votes
2 answers
17k views

Show function with infinitely many discontinuities is Riemann-integrable

10 votes
1 answer
4k views

If a normed space $X$ is reflexive, show that $X'$ is reflexive.

10 votes
1 answer
2k views

Full subcategory of abelian category is abelian

8 votes
2 answers
5k views

Functor preserves kernels iff it's left exact

8 votes
1 answer
3k views

Prove $(2, x)$ is not a free $R$-module.

8 votes
2 answers
5k views

Stalks of Skyscraper Sheaf

8 votes
3 answers
704 views

Open Source Abstract Algebra Textbooks

8 votes
4 answers
13k views

Prove that if $S$ is a finite set then $S$ has no limit points.

8 votes
2 answers
9k views

Determine the number of irreducible monic polynomials of degree 3 in $\mathbb F_p[x]$

8 votes
4 answers
1k views

Show $x^6 + 1.5x^5 + 3x - 4.5$ is irreducible in $\mathbb Q[x]$.

7 votes
3 answers
4k views

Irreducible $f(x) \in F[x]$ of prime degree, $E/F$ finite extension, $p \mid [E:F]$.

7 votes
2 answers
7k views

$f$ bounded on $[a,b]$ with one or finite discontinuities implies $f$ Riemann-integrable.

7 votes
2 answers
2k views

$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$

6 votes
2 answers
3k views

Ways $S_3$ can act on a set of 4 elements.

6 votes
3 answers
421 views

$G$ group, $H \trianglelefteq G$, $\vert H \vert$ prime, then $H \leq Z(G)$

6 votes
4 answers
548 views

Show that $(A / \mathfrak{a}) \otimes_A M \cong M / \mathfrak{a} M$ for a ring $A$, ideal $\mathfrak{a}$, $A$-module $M$.

6 votes
1 answer
1k views

Monotone Class Theorem for Functions

5 votes
1 answer
638 views

Equivalence of Schwartz Space Definition

5 votes
0 answers
347 views

Exercises in Topological K-Theory (Atiyah)

5 votes
2 answers
3k views

Prove that there are no simple groups of order 224.

5 votes
1 answer
2k views

$G$ topological group, $H$ discrete normal subgroup, $p$ projection, form Covering Space.

4 votes
1 answer
501 views

Show zero section is global section

4 votes
1 answer
116 views

No field properly between $\mathbb Q$ and $E$ iff $G(K/\mathbb Q) \cong A_4$ or $S_4$

4 votes
1 answer
3k views

Uncountable $\sigma$-algebra

4 votes
1 answer
469 views

Equivalent Definition of Continuity

4 votes
3 answers
460 views

$E/\mathbb F_q$ extension field. Show $[\mathbb F_q(\alpha) : \mathbb F_q]$ is smallest $n$ satisfying property.

3 votes
3 answers
374 views

Show $\vert G \vert = \vert HK \vert$ given that $H \trianglelefteq G$, $G$ finite and $K \leq G$.

3 votes
1 answer
4k views

Show $\mathbb R^n$ is complete.