List questions from group-isomorphism

Published on 10 May 2026 - 13:23

90

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Consider the groups $\mathbb{S_4}$, $\mathbb{D_6 \times C_2}$ and $\mathbb{A_4 \times C_2}$. Are of any of these two isomorphic?

Published on 13 May 2026 - 18:39

58

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Is this group the 4-permutation group?

Published on 14 Apr 2026 - 6:45

339

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How do I prove that $S_3 \times \mathbb{Z}_2$ is isomorphic to $D_6$?

Published on 10 Apr 2026 - 19:35

405

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Prove that there is a Galois extension $E$ of $\mathbb{Q}$ such that Gal$(E/\mathbb{Q}) \cong \mathbb{Z}_{18}$

Published on 14 May 2026 - 5:18

59

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Algebraic version of a manifold

Published on 15 Apr 2026 - 12:58

287

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Show the Galois group of $f(x)=x^p - 2$ is isomorphic to $\mathbb{Z}_p$

Published on 13 May 2026 - 18:04

87

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Writing the symmetry group of a cube without using direct products

Published on 12 May 2026 - 19:37

1.3k

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$f \colon G_1 \to G_2$ group homomorphism, then $G_1 / N_1 \cong G_2 / N_2$

Published on 10 May 2026 - 16:35

457

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Isomorphism of groups with complex numbers

Published on 11 Apr 2026 - 15:41

447

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Way to show automorphism of abelian group.

Published on 10 May 2026 - 19:38

92

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Prove that finite and infinite presentations of Thompson group $F$ are isomorphic.

Published on 10 May 2026 - 12:54

77

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I'm confused about exactly how a subgroup of $\Bbb Z \times \Bbb Z$ can be isomorphic to $\Bbb Z$

Published on 14 Apr 2026 - 2:11

64

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Showing that an isomorphism exists between $\Bbb Z$ and a subgroup of $\Bbb Z \times \Bbb Z$.

Published on 10 May 2026 - 15:03

489

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Characteristic subgroups of normal subgroups are normal

Published on 10 May 2026 - 21:47

List Question

Cancellation for finitely generated abelian groups

Consider the groups $\mathbb{S_4}$, $\mathbb{D_6 \times C_2}$ and $\mathbb{A_4 \times C_2}$. Are of any of these two isomorphic?

Is this group the 4-permutation group?

How do I prove that $S_3 \times \mathbb{Z}_2$ is isomorphic to $D_6$?

Prove that there is a Galois extension $E$ of $\mathbb{Q}$ such that Gal$(E/\mathbb{Q}) \cong \mathbb{Z}_{18}$

Algebraic version of a manifold

Show the Galois group of $f(x)=x^p - 2$ is isomorphic to $\mathbb{Z}_p$

Writing the symmetry group of a cube without using direct products

$f \colon G_1 \to G_2$ group homomorphism, then $G_1 / N_1 \cong G_2 / N_2$

Isomorphism of groups with complex numbers

Way to show automorphism of abelian group.

Prove that finite and infinite presentations of Thompson group $F$ are isomorphic.

I'm confused about exactly how a subgroup of $\Bbb Z \times \Bbb Z$ can be isomorphic to $\Bbb Z$

Showing that an isomorphism exists between $\Bbb Z$ and a subgroup of $\Bbb Z \times \Bbb Z$.

Characteristic subgroups of normal subgroups are normal

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