List questions from cyclotomic-fields

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165

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Why in cyclotomic extension, Gal($K/F$) may not isomorphic to the whole $Z/nZ$?

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49

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Proof of a relation of Stickelberger element

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103

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subfields of the cyclotomic fields $\mathbb{Q}(\zeta_p)$ with $p \equiv 1 [5]$

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141

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Fermat's Little Theorem in cyclotomic fields

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54

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Congruence in cyclotomic fields

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78

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The action of a Galois group on a cyclotomic field.

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251

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Factoring Primes in cyclotomic fields

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91

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Group of Units a Subgroup of some ${S}_n$

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106

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Algebraic Integers of a Field

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182

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On the irreducibility over cyclotomic field in radical extension.

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69

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Proving that $\mathbb{Z}[e^{2i\pi/23}]$ is not a PID

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68

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Minimal polynomial of $\eta_4$ over $\mathbb{Q}(\eta_2)$.

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Evaluate sum roots of unity $\zeta_{17}+\zeta_{17}^{-1}+\zeta_{17}^{2}+\zeta_{17}^{-2}+\zeta_{17}^{4}+\zeta_{17}^{-4}+\zeta_{17}^{8}+\zeta_{17}^{-8}$

Published on 25 Mar 2026 - 8:13

67

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Prove that $(1 - \omega)^{\phi(m)} = p$ where $\omega = e^{2\pi i/m}$

Published on 25 Mar 2026 - 8:09

List Question

Proof of a relation of elements in group rings

Why in cyclotomic extension, Gal($K/F$) may not isomorphic to the whole $Z/nZ$?

Proof of a relation of Stickelberger element

subfields of the cyclotomic fields $\mathbb{Q}(\zeta_p)$ with $p \equiv 1 [5]$

Fermat's Little Theorem in cyclotomic fields

Congruence in cyclotomic fields

The action of a Galois group on a cyclotomic field.

Factoring Primes in cyclotomic fields

Group of Units a Subgroup of some ${S}_n$

Algebraic Integers of a Field

On the irreducibility over cyclotomic field in radical extension.

Proving that $\mathbb{Z}[e^{2i\pi/23}]$ is not a PID

Minimal polynomial of $\eta_4$ over $\mathbb{Q}(\eta_2)$.

Evaluate sum roots of unity $\zeta_{17}+\zeta_{17}^{-1}+\zeta_{17}^{2}+\zeta_{17}^{-2}+\zeta_{17}^{4}+\zeta_{17}^{-4}+\zeta_{17}^{8}+\zeta_{17}^{-8}$

Prove that $(1 - \omega)^{\phi(m)} = p$ where $\omega = e^{2\pi i/m}$

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