List questions from galois-extensions

Published on 17 Apr 2019 - 17:23

454

Views

A question regarding the Galois extension of the cyclotomic polynomial $\Phi_{15}$

Published on 18 Apr 2019 - 18:02

115

Views

Condition on Galois Group that makes polynomial irreducible

Published on 18 Apr 2019 - 22:26

271

Views

A problem about the field of rational functions over finite field

Published on 21 Apr 2019 - 12:29

1.2k

Views

Proving that a field extension is Galois

Published on 26 Apr 2019 - 3:30

688

Views

This matrix is diagonalizable over algebraic closure of $\Bbb F_p$ iff $(n,p)=1$

Published on 30 Apr 2019 - 6:16

1.2k

Views

Are all Galois extensions simple?

Published on 30 Apr 2019 - 17:31

439

Views

Which subfields of the Galois group of $x^4+8x^2+8x+4$ are Galois and find the splitting field polynomial

Published on 26 Mar 2026 - 21:10

232

Views

Prove that complex conjugation of $\mathbb{C}$ preserves the splitting field

Published on 01 May 2019 - 6:17

57

Views

Show that if Gal$\left(K/F\right)$ is a non-trivial $2$-group, then there is a quadratic extension of $F$ contained in $K$.

Published on 05 May 2019 - 13:36

96

Views

finite Galois extension

Published on 08 May 2019 - 19:21

34

Views

Simple extension finder for $x^p-2$

Published on 09 May 2019 - 16:43

235

Views

Check that the corresponding extensions are normal

Published on 13 May 2019 - 8:16

68

Views

A question about Galois extension and splitting field of an irreducible polynomial

Published on 14 May 2019 - 22:34

85

Views

Intermediate field and Galois extension.

Published on 15 May 2019 - 21:53

List Question

Show that $E/F$ is Galois extension

A question regarding the Galois extension of the cyclotomic polynomial $\Phi_{15}$

Condition on Galois Group that makes polynomial irreducible

A problem about the field of rational functions over finite field

Proving that a field extension is Galois

This matrix is diagonalizable over algebraic closure of $\Bbb F_p$ iff $(n,p)=1$

Are all Galois extensions simple?

Which subfields of the Galois group of $x^4+8x^2+8x+4$ are Galois and find the splitting field polynomial

Prove that complex conjugation of $\mathbb{C}$ preserves the splitting field

Show that if Gal$\left(K/F\right)$ is a non-trivial $2$-group, then there is a quadratic extension of $F$ contained in $K$.

finite Galois extension

Simple extension finder for $x^p-2$

Check that the corresponding extensions are normal

A question about Galois extension and splitting field of an irreducible polynomial

Intermediate field and Galois extension.

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