Question

Let $G$ be a finite abelian group. Show that there is a Galois extension $K/\Bbb Q$ with $\text{Gal}(K/\Bbb Q) \cong G$.

score 929 · Answer 1 · 2015-04-03 15:30:26

929

Views

Let $G$ be a finite abelian group. Show that there is a Galois extension $K/\Bbb Q$ with $\text{Gal}(K/\Bbb Q) \cong G$.

Published on 03 Apr 2015 - 15:30

score 62 · Answer 2 · 2015-04-04 06:27:29

62

Views

Determine $n$, $m$ for which $\Bbb Q_n \subseteq \Bbb Q_m$.

Published on 04 Apr 2015 - 6:27

score 35 · Answer 3 · 2015-04-08 16:48:35

35

Views

Solution to $(x+1)^M-2=0\mod(x^a-1,M)$ with $a|M$.

Published on 08 Apr 2015 - 16:48

score 262 · Answer 4 · 2015-04-17 17:50:10

262

Views

Q basis for splitting field

Published on 17 Apr 2015 - 17:50

score 115 · Answer 5 · 2015-04-22 22:27:41

115

Views

Roots of "almost cyclotomic" polynomials

Published on 22 Apr 2015 - 22:27

score 248 · Answer 6 · 2015-04-29 17:37:16

248

Views

Let $\zeta=e^{2\pi i/n}$ Prove that $x^n -1 =(x-1)(x-\zeta)(x-\zeta^2) \dots (x-\zeta^{n-1})$

Published on 29 Apr 2015 - 17:37

score 84 · Answer 7 · 2015-05-10 22:27:42

84

Views

Irreducible polynomials in $\Bbb F_{2}[x]$ and their generators.

Published on 10 May 2015 - 22:27

score 1.3k · Answer 8 · 2015-05-11 18:47:50

1.3k

Views

proof that $\frac{x^p - 1}{x-1} = 1 + x + \dots + x^{p-1}$ is irreducible

Published on 11 May 2015 - 18:47

score 2.6k · Answer 9 · 2015-05-21 03:50:55

2.6k

Views

for $n > 1$ : odd , prove that $\Phi_{2n}(x) = \Phi_{n}(-x)$

Published on 21 May 2015 - 3:50

score 385 · Answer 10 · 2015-06-09 20:17:09

385

Views

Primitive roots of unity proof verification

Published on 09 Jun 2015 - 20:17

score 456 · Answer 11 · 2015-06-12 13:48:00

456

Views

Distinguishing Primitive vs. Nonprimitive Roots of Unity

Published on 12 Jun 2015 - 13:48

score 145 · Answer 12 · 2015-06-13 18:56:03

145

Views

For any integer $n$ there exists a prime $p$ such that the group $Z_p^*$ contains an element of order $n$

Published on 13 Jun 2015 - 18:56

score 440 · Answer 13 · 2015-06-14 08:04:54

440

Views

Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$

Published on 14 Jun 2015 - 8:04

score 905 · Answer 14 · 2015-06-14 12:53:53

905

Views

A unit of seventh cyclotomic field

Published on 14 Jun 2015 - 12:53

score 61 · Answer 15 · 2015-06-14 13:39:06

61

Views

Is there a relationship between these polynomial concepts?

Published on 14 Jun 2015 - 13:39

List Question

Let $G$ be a finite abelian group. Show that there is a Galois extension $K/\Bbb Q$ with $\text{Gal}(K/\Bbb Q) \cong G$.

Determine $n$, $m$ for which $\Bbb Q_n \subseteq \Bbb Q_m$.

Solution to $(x+1)^M-2=0\mod(x^a-1,M)$ with $a|M$.

Q basis for splitting field

Roots of "almost cyclotomic" polynomials

Let $\zeta=e^{2\pi i/n}$ Prove that $x^n -1 =(x-1)(x-\zeta)(x-\zeta^2) \dots (x-\zeta^{n-1})$

Irreducible polynomials in $\Bbb F_{2}[x]$ and their generators.

proof that $\frac{x^p - 1}{x-1} = 1 + x + \dots + x^{p-1}$ is irreducible

for $n > 1$ : odd , prove that $\Phi_{2n}(x) = \Phi_{n}(-x)$

Primitive roots of unity proof verification

Distinguishing Primitive vs. Nonprimitive Roots of Unity

For any integer $n$ there exists a prime $p$ such that the group $Z_p^*$ contains an element of order $n$

Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$

A unit of seventh cyclotomic field

Is there a relationship between these polynomial concepts?

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