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Show that no root of the polynomial $x^5 + 21x^4 - 14x^3 + 28x^2 - 7x + 42$ is constructible.

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#abstract-algebra #galois-theory #irreducible-polynomials #geometric-construction #galois-extensions
61
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Intermediate extensions of Hilbert class field

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#abstract-algebra #number-theory #galois-theory #galois-extensions
795
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Minimal polynomial for some galois extension

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#abstract-algebra #galois-theory #minimal-polynomials #galois-extensions
710
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Is complex $\mathbb{C}$ a Galois extension of rationals $\mathbb{Q}$?

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#abstract-algebra #galois-extensions
61
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Quadratic Extensions of an element g

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#abstract-algebra #extension-field #galois-extensions
649
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Exercise 14.7.4 in dummit and foote

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#field-theory #proof-explanation #galois-theory #galois-extensions
59
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Separable extension of $k \subset K \subset L$

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#galois-theory #extension-field #galois-extensions #separable-extension
644
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Finding the fixed subfield of an automorphism subgroup of $k(x)$.

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#field-theory #galois-theory #extension-field #galois-extensions #separable-extension
77
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Subgroup inavariant subextension of Galois extension

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#abstract-algebra #galois-theory #extension-field #galois-extensions
191
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A Question on Stabilizers

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#group-theory #galois-theory #galois-extensions
110
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In profinite group $G$ with inverse system $(G_\alpha)%$, how the kernel of projection map becomes the basis of neighborhood for $1$ in $G$?

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#abstract-algebra #galois-theory #fundamental-groups #galois-extensions #profinite-groups
646
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Galois group of splitting field of $X^4-6X^2+7$ is non-abelian

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#galois-theory #splitting-field #galois-extensions
249
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All intermediate subfields

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#abstract-algebra #galois-theory #galois-extensions
58
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Question about algebraic extensions.

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#galois-theory #extension-field #galois-extensions
267
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A question about algebraic extension and how to extend an automorphism

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#abstract-algebra #galois-theory #extension-field #galois-extensions

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