Question

Operations used in the isomorphism theorem

score 41 · Answer 1 · 2020-03-31 00:35:28

41

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Operations used in the isomorphism theorem

Published on 31 Mar 2020 - 0:35

score 55 · Answer 2 · 2026-03-28 07:53:35

55

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Given a specific 2 by 2 matrix that is a subset of all 2 by 2 real matrices find an isomorphisim between the matrix and complex number system

Published on 28 Mar 2026 - 7:53

score 485 · Answer 3 · 2026-03-24 23:45:45

485

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Finding a subgroup of $S_5$ that is isomorphic to $D_5$

Published on 24 Mar 2026 - 23:45

score 74 · Answer 4 · 2020-04-01 16:24:40

74

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Proving Isomorphism between $G$ and its dual $\hat{G}$

Published on 01 Apr 2020 - 16:24

score 195 · Answer 5 · 2020-04-08 10:56:57

195

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Given $\phi\colon G\rightarrow G'$ onto, does $\phi(G)=G'$?

Published on 08 Apr 2020 - 10:56

score 607 · Answer 6 · 2026-03-26 12:40:27

607

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Prove that $G/N$ is isomorphic to $(G/K)/(N/K).$

Published on 26 Mar 2026 - 12:40

score 59 · Answer 7 · 2026-03-28 09:28:32

59

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Let $f:G \rightarrow G$ is automorphism. If $N(g) = \lbrace x \in G | xg=gx, \forall g \in G \rbrace$. Prove that $f(N(g)) = N(f(g))$.

Published on 28 Mar 2026 - 9:28

score 49 · Answer 8 · 2026-03-28 18:17:07

49

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How to prove that $\mathbb{Z}_p^\times$ is isomorphic to $(\mathbb{Z}_p, +) \times \mathbb{F}_p^\times$?

Published on 28 Mar 2026 - 18:17

score 110 · Answer 9 · 2026-03-28 09:34:17

110

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Consider the map $\psi : G \rightarrow Aut(G)$ given by $\psi(g) = \phi_{g}.$ Prove that $\psi$ is a homomorphism

Published on 28 Mar 2026 - 9:34

score 191 · Answer 10 · 2026-03-29 15:16:36

191

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Cayley classic theorem: Every group $G$ is isomorphic to a subgroup of $\operatorname{Sym}(G)$.

Published on 29 Mar 2026 - 15:16

score 69 · Answer 11 · 2020-04-17 13:17:44

69

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Relationship between Galois Correspondence and the Fourth Isomorphism Theorem (Correspondence Theorem)?

Published on 17 Apr 2020 - 13:17

score 67 · Answer 12 · 2020-04-17 22:05:05

67

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Prove that $f(H)=\{y\in G∶y=f(x)\text{ for some }x\in H\}\le G.$

Published on 17 Apr 2020 - 22:05

score 55 · Answer 13 · 2026-03-28 09:34:22

55

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If $T=\lbrace -1,1 \rbrace$, show that $\mathbb{R}^{*}/\mathbb{R}^{+} \cong T$ is group under multiplication.

Published on 28 Mar 2026 - 9:34

score 93 · Answer 14 · 2020-04-18 23:52:08

93

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Prove that $g∶ H \to f(H),$ given by $g(x)=f(x)$ is an isomorphism, given $f$ is an isomorphism.

Published on 18 Apr 2020 - 23:52

score 106 · Answer 15 · 2020-04-19 10:09:15

106

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Sufficient conditions for square map to be group isomorphism, with basic tools

Published on 19 Apr 2020 - 10:09

List Question

Operations used in the isomorphism theorem

Given a specific 2 by 2 matrix that is a subset of all 2 by 2 real matrices find an isomorphisim between the matrix and complex number system

Finding a subgroup of $S_5$ that is isomorphic to $D_5$

Proving Isomorphism between $G$ and its dual $\hat{G}$

Given $\phi\colon G\rightarrow G'$ onto, does $\phi(G)=G'$?

Prove that $G/N$ is isomorphic to $(G/K)/(N/K).$

Let $f:G \rightarrow G$ is automorphism. If $N(g) = \lbrace x \in G | xg=gx, \forall g \in G \rbrace$. Prove that $f(N(g)) = N(f(g))$.

How to prove that $\mathbb{Z}_p^\times$ is isomorphic to $(\mathbb{Z}_p, +) \times \mathbb{F}_p^\times$?

Consider the map $\psi : G \rightarrow Aut(G)$ given by $\psi(g) = \phi_{g}.$ Prove that $\psi$ is a homomorphism

Cayley classic theorem: Every group $G$ is isomorphic to a subgroup of $\operatorname{Sym}(G)$.

Relationship between Galois Correspondence and the Fourth Isomorphism Theorem (Correspondence Theorem)?

Prove that $f(H)=\{y\in G∶y=f(x)\text{ for some }x\in H\}\le G.$

If $T=\lbrace -1,1 \rbrace$, show that $\mathbb{R}^{*}/\mathbb{R}^{+} \cong T$ is group under multiplication.

Prove that $g∶ H \to f(H),$ given by $g(x)=f(x)$ is an isomorphism, given $f$ is an isomorphism.

Sufficient conditions for square map to be group isomorphism, with basic tools

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