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Is there a general method to find the size of the Galois group of a cubic polynomial over $\mathbb{Q}$?

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#abstract-algebra #field-theory #galois-theory #extension-field #galois-extensions
204
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What is the relationship between Gal($K_1/F_1$) and Gal$(K_2/F_2)$?

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#abstract-algebra #galois-theory #extension-field #galois-extensions
65
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Is $\mathbb{F}_{p^r}/\mathbb{F}_{p}$ a Galois extension?

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#abstract-algebra #galois-theory #finite-fields #galois-extensions
40
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Calculating Galois groups of Quartics

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#galois-theory #extension-field #galois-extensions
41
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Galois fields and irreducible polynomials

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#galois-theory #galois-extensions
100
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How to Show that E:Q is a Galois Extension?

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#galois-theory #splitting-field #galois-extensions
131
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Fixed ring $\mathbb{Z}[\zeta]^\tau$ is the ring of integers of the fixed field $\mathbb{Q}(\zeta)^\tau$

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#number-theory #ring-theory #galois-theory #cyclotomic-fields #galois-extensions
129
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What is the Galois Group of $X^5 + 5 X^3+5 X^2+4 X+1 \in \mathbb{Q}[X]$?

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#polynomials #galois-theory #irreducible-polynomials #galois-extensions
135
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How to find Galois extension given the Galois group?

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#galois-theory #galois-extensions
198
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Constructing composite Galois field with arbitrary primitive polynomial?

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#field-theory #galois-theory #finite-fields #galois-extensions
545
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What are the intermediate fields of $\mathbb{Q}(\sqrt[4]{2},i)/\mathbb{Q}$ of order $4$ over $\mathbb{Q}$?

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#galois-theory #irreducible-polynomials #primitive-roots #cyclotomic-polynomials #galois-extensions
42
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Normal closure $L/k$ contains the Galois image of $k$

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#field-theory #galois-theory #galois-extensions
770
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What is the Galois group of $f = X^4 - 3X^2+3 \in \mathbb{Q}[X]$?

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#polynomials #galois-theory #irreducible-polynomials #minimal-polynomials #galois-extensions
737
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Galois group of $x^3+2x+2$

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#field-theory #galois-theory #extension-field #splitting-field #galois-extensions
194
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Find Galois group of $\mathbb{Q} ( \sqrt{p})/\mathbb{Q}$

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#field-theory #galois-theory #extension-field #galois-extensions

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