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Splitting field of $x^5 - t$ over $\mathbb{F}_{11}(t)$

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#abstract-algebra #polynomials #field-theory #finite-fields #extension-field
137
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Generating set of the permutation group

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#abstract-algebra #polynomials #permutations #finite-fields
1.2k
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Generator of multiplicative group of the finite field

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#abstract-algebra #finite-fields
111
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Quadratic Gauss Sums to prove law of quadratic reciprocity

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#finite-fields
193
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Isomorphic Factor Rings of Z_2[x]

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#abstract-algebra #ring-theory #field-theory #ideals #finite-fields
138
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General way to find monic irreducible polynomial of degree $n$

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#abstract-algebra #finite-fields #irreducible-polynomials
255
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Generators and commutator Subgroup of $SL(2,3)$

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#group-theory #finite-fields #linear-groups
43
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Characteristic of a field is a minimal number

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#field-theory #finite-fields
115
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Size of a field with field extensions is hopefully equal to $p^n-1$

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#abstract-algebra #field-theory #finite-fields #extension-field
30
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Finding an isomorphism between finite fields of same order, but different construction.

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#finite-fields #group-isomorphism #ring-isomorphism
53
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How do I check whether a polynomial is separable over a function field?

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#abstract-algebra #polynomials #galois-theory #finite-fields
64
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Is $x^5+x^3+x+1$ irreducible in $\mathbb{F}_3$?

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#field-theory #galois-theory #finite-fields #irreducible-polynomials
195
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Is $\mathbf F_3(t,t^{1/3})/\mathbf F_3(t)$ a normal extension? Is it separable?

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#abstract-algebra #galois-theory #finite-fields
48
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Systems of matrices

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#matrices #finite-fields
82
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What will be $\text {Ord}_n\ q$?

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#field-theory #galois-theory #finite-fields #cyclotomic-polynomials

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