List questions from group-isomorphism

Published on 28 Mar 2026 - 9:50

793

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Show that G is isomorphic to C4

Published on 29 Mar 2026 - 16:47

58

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The use of Isomorphic Theorems

Published on 12 Nov 2019 - 17:48

29

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Finding an isomorphism between finite fields of same order, but different construction.

Published on 25 Feb 2026 - 0:31

626

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What is U(1)/Z2 isomorphic to?

Published on 27 Mar 2026 - 19:58

46

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Suppose $\mathbb{Z}/m\mathbb{Z}$ is a subgroup of $S_n$. Then $D_{2m}$ is too.

Published on 26 Mar 2026 - 12:48

176

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Isomorphism between $\mathbb{R}$ and $\mathbb{C}$ as additive 'groups'

Published on 30 Mar 2026 - 3:17

87

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Questions about isomorphic properties using $\mathbb Z_4 , \mathbb Z_2 \times \mathbb Z_2 , P_2 $, and $V$ as examples.

Published on 16 Nov 2019 - 4:00

37

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No homeomorphism.

Published on 17 Nov 2019 - 13:05

190

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Prove that $T/J$ is isomorphic to $\mathbb{R} \times \mathbb{R}$ as a ring.

Published on 17 Nov 2019 - 18:16

28

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Isomorphism of groups involving quotients

Published on 17 Nov 2019 - 21:11

116

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Seeking a general example of $f \in S_G$ but $f \notin {\rm Aut}(G)$

Published on 29 Mar 2026 - 4:55

920

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Automorphism Group isomorphic to $\mathbb{Z}_n$

Published on 29 Mar 2026 - 4:53

206

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If $G = H$ is a non-trivial group, is it possible for $G*H$ to be isomorphic to $\mathbb Z^2$

Published on 25 Mar 2026 - 14:36

1k

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Irreducible representations of a semidirect product, proof in Serre

Published on 25 Mar 2026 - 20:15

List Question

Show that ${\rm Aut}(Z_2 \times Z_2) \cong S_3$

Show that G is isomorphic to C4

The use of Isomorphic Theorems

Finding an isomorphism between finite fields of same order, but different construction.

What is U(1)/Z2 isomorphic to?

Suppose $\mathbb{Z}/m\mathbb{Z}$ is a subgroup of $S_n$. Then $D_{2m}$ is too.

Isomorphism between $\mathbb{R}$ and $\mathbb{C}$ as additive 'groups'

Questions about isomorphic properties using $\mathbb Z_4 , \mathbb Z_2 \times \mathbb Z_2 , P_2 $, and $V$ as examples.

No homeomorphism.

Prove that $T/J$ is isomorphic to $\mathbb{R} \times \mathbb{R}$ as a ring.

Isomorphism of groups involving quotients

Seeking a general example of $f \in S_G$ but $f \notin {\rm Aut}(G)$

Automorphism Group isomorphic to $\mathbb{Z}_n$

If $G = H$ is a non-trivial group, is it possible for $G*H$ to be isomorphic to $\mathbb Z^2$

Irreducible representations of a semidirect product, proof in Serre

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