Question

$FG$-modules $V$ and $W$ isomorphic and its properties

score 172 · Answer 1 · 2026-04-17 08:11:24

172

Views

$FG$-modules $V$ and $W$ isomorphic and its properties

Published on 17 Apr 2026 - 8:11

score 128 · Answer 2 · 2026-05-11 08:33:40

128

Views

Show that Jordan Block $\iff V$ isomorphic to $K[X]/(X-\lambda)^{n}$ as a $K[X]$-Module

Published on 11 May 2026 - 8:33

score 103 · Answer 3 · 2026-04-12 19:04:51

103

Views

Isomorphism preserving operations

Published on 12 Apr 2026 - 19:04

score 108 · Answer 4 · 2026-05-11 01:53:25

108

Views

Let $A$ be the group of anti-automorphisms, $B=A\cup \operatorname{Aut}(G)$, prove $B\cong A\times \mathbb{Z}/2\mathbb{Z}$

Published on 11 May 2026 - 1:53

score 2.4k · Answer 5 · 2026-04-17 10:06:15

2.4k

Views

Are the groups $\Bbb Z/8\Bbb Z$, $ (\Bbb Z/2\Bbb Z) \times (\Bbb Z/4\Bbb Z)$ and $(\Bbb Z/2\Bbb Z)^3$ isomorphic?

Published on 17 Apr 2026 - 10:06

score 1k · Answer 6 · 2026-05-10 13:48:35

1k

Views

Isomorphism from inner direct product to external.

Published on 10 May 2026 - 13:48

score 14.8k · Answer 7 · 2026-05-10 21:50:09

14.8k

Views

Listing methods to prove that two groups are not isomorphic

Published on 10 May 2026 - 21:50

score 6.6k · Answer 8 · 2026-04-11 10:30:37

6.6k

Views

How to prove that $\mathbb{Z/2Z\times Z/2Z}$ is not cyclic?

Published on 11 Apr 2026 - 10:30

score 799 · Answer 9 · 2026-04-13 23:57:21

799

Views

How to show that $Z/12Z×Z/90Z×Z/25Z$ and $Z/100Z×Z/30Z×Z/9Z$ are isomorph?

Published on 13 Apr 2026 - 23:57

score 54 · Answer 10 · 2026-05-10 16:06:23

54

Views

Isomorphism of quotients over isomorphic commutators

Published on 10 May 2026 - 16:06

score 79 · Answer 11 · 2026-04-08 23:38:43

79

Views

$\mathbb{Z} \times \mathbb{Z}$ and application of isomorphism theorems

Published on 08 Apr 2026 - 23:38

score 268 · Answer 12 · 2026-05-11 00:43:07

268

Views

Two points from the same topological space that their fundamental group is not isomorphic.

Published on 11 May 2026 - 0:43

score 115 · Answer 13 · 2026-05-10 14:31:30

115

Views

Prove that $(\mathbb{Z}[x]/(x^2))^\times \cong \mathbb{Z} \times \mathbb{Z}_2.$

Published on 10 May 2026 - 14:31

score 49 · Answer 14 · 2026-05-11 01:47:54

49

Views

Differentiating biholomorphic functions gives isomorphism $Aut_{z_0}(U) \cong S^1$

Published on 11 May 2026 - 1:47

score 341 · Answer 15 · 2026-05-10 14:07:31

341

Views

Prove that the groups $\langle a,b \mid ababa=babab \rangle$ and $\langle x,y \mid x^2=y^5 \rangle$ are isomorphic

Published on 10 May 2026 - 14:07

List Question

$FG$-modules $V$ and $W$ isomorphic and its properties

Show that Jordan Block $\iff V$ isomorphic to $K[X]/(X-\lambda)^{n}$ as a $K[X]$-Module

Isomorphism preserving operations

Let $A$ be the group of anti-automorphisms, $B=A\cup \operatorname{Aut}(G)$, prove $B\cong A\times \mathbb{Z}/2\mathbb{Z}$

Are the groups $\Bbb Z/8\Bbb Z$, $ (\Bbb Z/2\Bbb Z) \times (\Bbb Z/4\Bbb Z)$ and $(\Bbb Z/2\Bbb Z)^3$ isomorphic?

Isomorphism from inner direct product to external.

Listing methods to prove that two groups are not isomorphic

How to prove that $\mathbb{Z/2Z\times Z/2Z}$ is not cyclic?

How to show that $Z/12Z×Z/90Z×Z/25Z$ and $Z/100Z×Z/30Z×Z/9Z$ are isomorph?

Isomorphism of quotients over isomorphic commutators

$\mathbb{Z} \times \mathbb{Z}$ and application of isomorphism theorems

Two points from the same topological space that their fundamental group is not isomorphic.

Prove that $(\mathbb{Z}[x]/(x^2))^\times \cong \mathbb{Z} \times \mathbb{Z}_2.$

Differentiating biholomorphic functions gives isomorphism $Aut_{z_0}(U) \cong S^1$

Prove that the groups $\langle a,b \mid ababa=babab \rangle$ and $\langle x,y \mid x^2=y^5 \rangle$ are isomorphic

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