Question

proving $x$ is the generator of a cyclic group

score 194 · Answer 1 · 2026-03-28 21:26:50

194

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proving $x$ is the generator of a cyclic group

Published on 28 Mar 2026 - 21:26

score 10.6k · Answer 2 · 2026-03-27 00:05:16

10.6k

Views

Does every subgroup of an abelian group have to be abelian?

Published on 27 Mar 2026 - 0:05

score 86 · Answer 3 · 2019-04-24 06:34:34

86

Views

Is $Aut(K/\mathbb F_q)$ finite?

Published on 24 Apr 2019 - 6:34

score 125 · Answer 4 · 2026-03-25 22:11:02

125

Views

Cyclotomic polynomials of distinct index are distinct.

Published on 25 Mar 2026 - 22:11

score 1k · Answer 5 · 2026-03-27 01:47:46

1k

Views

For any finite abelian group $G$, there is an integer $m$ with $G$ isomorphic to a subgroup of $U(\mathbb{Z}_{m})$.

Published on 27 Mar 2026 - 1:47

score 163 · Answer 6 · 2019-04-25 21:50:22

163

Views

Find the invariant of a subgroup of automorphisms on $\mathbb Q(X)$

Published on 25 Apr 2019 - 21:50

score 1.2k · Answer 7 · 2026-03-28 01:02:53

1.2k

Views

Proving that a field extension is Galois

Published on 28 Mar 2026 - 1:02

score 306 · Answer 8 · 2019-04-26 13:03:24

306

Views

Subgroup of squares in $(\mathbf{Z}/p\mathbf{Z})^*$ is of index 2

Published on 26 Apr 2019 - 13:03

score 147 · Answer 9 · 2019-04-26 13:38:06

147

Views

Infinitude of abelian extensions of $\mathbb{Q}$ with given Galois group $G$

Published on 26 Apr 2019 - 13:38

score 46 · Answer 10 · 2019-04-26 14:28:07

46

Views

Prove $\operatorname{Gal}(\mathbb{Q}(e^{\pi i/q}):\mathbb{Q}) \cong C_{q-1}$ for odd prime q.

Published on 26 Apr 2019 - 14:28

score 414 · Answer 11 · 2026-03-25 05:06:52

414

Views

Basis of $\mathbb{Q}(\sqrt[3]{2},\omega)$ over $\mathbb{Q}$

Published on 25 Mar 2026 - 5:06

score 89 · Answer 12 · 2019-04-28 10:12:36

89

Views

Why does the Galois correspondence not hold for non normal/separable extensions

Published on 28 Apr 2019 - 10:12

score 309 · Answer 13 · 2019-04-28 15:10:28

309

Views

Understand a proof in Galois theory

Published on 28 Apr 2019 - 15:10

score 127 · Answer 14 · 2026-03-29 08:16:11

127

Views

Is it true that irrational roots of rational polynomial comes in pairs? How to prove this? If not give an example please.

Published on 29 Mar 2026 - 8:16

score 79 · Answer 15 · 2019-04-29 01:23:16

79

Views

Given two numbers $u$ and $v$, prove there exist (possibly complex) numbers $y$ and $z$ such that $y+z=u$ and $yz=v$.

Published on 29 Apr 2019 - 1:23

List Question

proving $x$ is the generator of a cyclic group

Does every subgroup of an abelian group have to be abelian?

Is $Aut(K/\mathbb F_q)$ finite?

Cyclotomic polynomials of distinct index are distinct.

For any finite abelian group $G$, there is an integer $m$ with $G$ isomorphic to a subgroup of $U(\mathbb{Z}_{m})$.

Find the invariant of a subgroup of automorphisms on $\mathbb Q(X)$

Proving that a field extension is Galois

Subgroup of squares in $(\mathbf{Z}/p\mathbf{Z})^*$ is of index 2

Infinitude of abelian extensions of $\mathbb{Q}$ with given Galois group $G$

Prove $\operatorname{Gal}(\mathbb{Q}(e^{\pi i/q}):\mathbb{Q}) \cong C_{q-1}$ for odd prime q.

Basis of $\mathbb{Q}(\sqrt[3]{2},\omega)$ over $\mathbb{Q}$

Why does the Galois correspondence not hold for non normal/separable extensions

Understand a proof in Galois theory

Is it true that irrational roots of rational polynomial comes in pairs? How to prove this? If not give an example please.

Given two numbers $u$ and $v$, prove there exist (possibly complex) numbers $y$ and $z$ such that $y+z=u$ and $yz=v$.

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