List questions from group-isomorphism

Published on 09 Nov 2015 - 3:29

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How to show $\phi$ is a bijection between two set of subgroups

Published on 01 Apr 2026 - 2:04

460

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can I conclude that image of a function is bijective to its domain by proving its injective?

Published on 10 Nov 2015 - 22:07

33

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Let $f = \prod_{i=1}^n (X - z_i)^{r_i} \in \mathbb{C}[x]$. Prove that $\mathbb{C}[x]/(f) \simeq \prod_{i=1}^n \mathbb{C}[x]/(X-z_i)^{r_i}$

Published on 30 Mar 2026 - 13:40

884

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How can you show that 2 (adjacency) matrices are isomorphic?

Published on 30 Mar 2026 - 22:43

1k

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How to prove that this ring homomorphism is isomorphic?

Published on 11 Nov 2015 - 23:39

90

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If $Aut(G)$ is cyclic, how is its generator defined?

Published on 02 Apr 2026 - 4:50

6.5k

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${\rm Aut}(G)$ is cyclic $\implies G$ is abelian

Published on 30 Mar 2026 - 10:17

386

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If $G$ is finite abelian and there exists an element of order $> 2$ then $|Aut(G)|$ is even

Published on 12 Nov 2015 - 22:43

92

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$\text{Aut}(G) \cong \text{Out}(G)$ when $G$ is abelian

Published on 12 Nov 2015 - 23:29

57

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Showing that $G$ is isomorphic to $\{1,-1\}\times \mathbb{R}$

Published on 28 Mar 2026 - 12:14

247

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Finite Quotient Groups

Published on 14 Nov 2015 - 1:00

146

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Group Theory: let $G$ be a group and let $G=H\times K$, is it true that $G/H\cong K$?

Published on 02 Apr 2026 - 10:16

614

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Are finite groups with same conjugacy classes isomorphic

Published on 15 Nov 2015 - 20:42

360

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Presentation of the special linear group $SL_2(\mathbb{Z})\cong G=\langle a,b|a^4=1,a^2b^{-3}=1\rangle$

Published on 18 Mar 2026 - 23:56

List Question

|Aut(G)| dependent on orders of elements of G?

How to show $\phi$ is a bijection between two set of subgroups

can I conclude that image of a function is bijective to its domain by proving its injective?

Let $f = \prod_{i=1}^n (X - z_i)^{r_i} \in \mathbb{C}[x]$. Prove that $\mathbb{C}[x]/(f) \simeq \prod_{i=1}^n \mathbb{C}[x]/(X-z_i)^{r_i}$

How can you show that 2 (adjacency) matrices are isomorphic?

How to prove that this ring homomorphism is isomorphic?

If $Aut(G)$ is cyclic, how is its generator defined?

${\rm Aut}(G)$ is cyclic $\implies G$ is abelian

If $G$ is finite abelian and there exists an element of order $> 2$ then $|Aut(G)|$ is even

$\text{Aut}(G) \cong \text{Out}(G)$ when $G$ is abelian

Showing that $G$ is isomorphic to $\{1,-1\}\times \mathbb{R}$

Finite Quotient Groups

Group Theory: let $G$ be a group and let $G=H\times K$, is it true that $G/H\cong K$?

Are finite groups with same conjugacy classes isomorphic

Presentation of the special linear group $SL_2(\mathbb{Z})\cong G=\langle a,b|a^4=1,a^2b^{-3}=1\rangle$

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