List questions from symmetric-groups

Published on 14 Jan 2019 - 13:30

1.9k

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f irreducible polynomial with $p-2$ real roots $\Rightarrow$ $Gal(\mathbb{Q}_{f}/\mathbb{Q}) \cong S_{p}$

Published on 16 Jan 2019 - 1:58

333

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Group generated by $(1234567)$ and $(26)(34)$ is of order 168.

Published on 16 Jan 2019 - 11:41

514

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Let $\phi: S_n \to G$ be a homomorphism, where $|G|$ is odd. Prove that $\phi$ must be trivial.

Published on 16 Jan 2019 - 16:31

232

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List of symmetric group elements from the usual presentation

Published on 16 Jan 2019 - 23:48

160

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Is $A_4 \times \mathbb{Z}_3$ isomorphic to $S_3 \times S_3$?

Published on 18 Jan 2019 - 7:45

1k

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How do I find the order of a bijection?

Published on 18 Jan 2019 - 20:39

99

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Proving that $|S_8 \cdot a|=\binom{8}{4}\frac{4!}{4}$

Published on 20 Jan 2019 - 16:36

50

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Verifying the calculation of the number of conjugate elements

Published on 20 Jan 2019 - 18:00

125

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Equation with Galois group twisted $S_{3}$

Published on 22 Mar 2026 - 15:33

870

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Homomorphisms of $S_3$

Published on 21 Jan 2019 - 14:31

123

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Proving that $\text{Sym}(T)$ is a group without treating functions as sets

Published on 22 Jan 2019 - 20:47

241

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The monomial representation of $S_n$ is irreducible.

Published on 25 Mar 2026 - 14:33

640

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How to compute quickly the order of the automorphism group of $A_4$

Published on 25 Mar 2026 - 18:50

76

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Stabilizer in the definition of a Gelfand pair

Published on 28 Jan 2019 - 21:37

List Question

Unique Elements from Subsets of Symmetric Group

f irreducible polynomial with $p-2$ real roots $\Rightarrow$ $Gal(\mathbb{Q}_{f}/\mathbb{Q}) \cong S_{p}$

Group generated by $(1234567)$ and $(26)(34)$ is of order 168.

Let $\phi: S_n \to G$ be a homomorphism, where $|G|$ is odd. Prove that $\phi$ must be trivial.

List of symmetric group elements from the usual presentation

Is $A_4 \times \mathbb{Z}_3$ isomorphic to $S_3 \times S_3$?

How do I find the order of a bijection?

Proving that $|S_8 \cdot a|=\binom{8}{4}\frac{4!}{4}$

Verifying the calculation of the number of conjugate elements

Equation with Galois group twisted $S_{3}$

Homomorphisms of $S_3$

Proving that $\text{Sym}(T)$ is a group without treating functions as sets

The monomial representation of $S_n$ is irreducible.

How to compute quickly the order of the automorphism group of $A_4$

Stabilizer in the definition of a Gelfand pair

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