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15
107
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Splitting field as a minimal Galois extension

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#galois-theory #extension-field #splitting-field #galois-extensions
317
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Degree of a splitting field is no greater than $n!$

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#galois-theory #splitting-field #galois-extensions
79
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Correspondence between set of all $K$-linear homomorphisms and set of all irreducible idempotents

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#galois-theory #idempotents #galois-extensions
188
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Existence of intermediate fields with order $9$ and $3$ of a Galois field extension of order $27$.

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#abstract-algebra #field-theory #galois-theory #extension-field #galois-extensions
222
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Cyclotomic field

Published on
#galois-theory #cyclotomic-fields #galois-extensions
95
Views

Inverse Galois Problem: the two-fold central extension of $Sp_6(\mathbb F_2) \cong [W(E_7),W(E_7)]$

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#galois-theory #simple-groups #galois-representations #galois-extensions #weyl-group
89
Views

Cyclotomic field (again)

Published on
#galois-theory #cyclotomic-fields #galois-extensions
242
Views

Field homomorphisms and automorphisms

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#abstract-algebra #field-theory #galois-theory #extension-field #galois-extensions
952
Views

A Cyclic Extension of degree 4 does not contain $i$

Published on
#field-theory #galois-theory #galois-extensions
176
Views

Galois extension does not contain a cyclic extension of degree 3

Published on
#field-theory #galois-theory #galois-extensions
159
Views

If $H_2 \unlhd H_1$, then is $F_2$ Galois over $F_1$?

Published on
#abstract-algebra #field-theory #galois-theory #galois-extensions
201
Views

Problem with a proof of Wilson's 'Profinite groups'

Published on
#galois-theory #profinite-groups #galois-extensions
295
Views

Computing Galois group of a quartic polynomial

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#galois-theory #galois-extensions
158
Views

Prime ideals lying above a prime number in $\mathbb{Q}(\zeta_n)$

Published on
#field-theory #algebraic-number-theory #extension-field #galois-extensions
608
Views

Constructing type $k$ Gaussian normal basis for $GF(2^n)$

Published on
#finite-fields #galois-extensions

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