Question

Showing that the extension $1 \to C_3 \to C_6 \to C_2 \to 1$ is split by finding complement of $C_3$

score 66 · Answer 1 · 2026-03-27 07:17:13

66

Views

Showing that the extension $1 \to C_3 \to C_6 \to C_2 \to 1$ is split by finding complement of $C_3$

Published on 27 Mar 2026 - 7:17

score 413 · Answer 2 · 2026-03-26 17:32:44

413

Views

Direct product of groups of homomorphisms

Published on 26 Mar 2026 - 17:32

score 455 · Answer 3 · 2026-03-26 21:25:22

455

Views

Abstract Algebra ( tutoring suggestions )

Published on 26 Mar 2026 - 21:25

score 58 · Answer 4 · 2020-04-15 11:15:25

58

Views

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 15 Apr 2020 - 11:15

score 332 · Answer 5 · 2020-04-15 12:32:56

332

Views

Application of First Fundamental theorem on Isomorphism.

Published on 15 Apr 2020 - 12:32

score 109 · Answer 6 · 2020-04-15 19:27:54

109

Views

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

Published on 15 Apr 2020 - 19:27

score 54 · Answer 7 · 2020-04-18 23:13:21

54

Views

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

Published on 18 Apr 2020 - 23:13

score 41 · Answer 8 · 2020-04-19 08:33:29

41

Views

Let $f:\mathbb{Z} \rightarrow \mathbb{Z}_{10}$ is homomorphism. Determine $f(18)$ such that $f(1)=6$.

Published on 19 Apr 2020 - 8:33

score 37 · Answer 9 · 2020-04-21 03:04:42

General form of a group morphism $\tau : \mathbb{Z}_p \to \operatorname{Aut}(\mathbb{Z}_q)$ such that $\bar{k} \mapsto \tau_{\bar{k}}$

score 158 · Answer 10 · 2020-04-21 03:28:39

158

Views

Compute the kernel of the group hom $\Omega : \Bbb{Q}^{\times} \to \Bbb{Z}^+$.

Published on 21 Apr 2020 - 3:28

score 39 · Answer 11 · 2020-04-21 03:41:16

39

Views

If $f:\mathbb{Z}\times \mathbb{Z} \rightarrow \mathbb{Z} \times \mathbb{Z}$ is homomorphism, show that $f$ is monomorphism.

Published on 21 Apr 2020 - 3:41

score 38 · Answer 12 · 2020-04-21 04:35:32

38

Views

Condition for triviality of group morphism $\tau : \mathbb{Z}_p \to\mathrm{Aut}(\mathbb{Z}_q)$ : $\tau_\overline{k}(\overline{n}) = \bar{r}^k \bar{n}$

Published on 21 Apr 2020 - 4:35

score 85 · Answer 13 · 2020-04-21 10:59:16

85

Views

How would I prove the following theorem on quaternions?

Published on 21 Apr 2020 - 10:59

score 246 · Answer 14 · 2020-04-21 18:36:59

246

Views

Homomorphic image of an alternating group

Published on 21 Apr 2020 - 18:36

score 197 · Answer 15 · 2020-04-22 09:35:12

197

Views

Proof: If $ϕ: R \to R'$ is a ring isomorphism, then its inverse $ϕ^{-1} : R' \to R$ is a ring homomorphism.

Published on 22 Apr 2020 - 9:35

List Question

Showing that the extension $1 \to C_3 \to C_6 \to C_2 \to 1$ is split by finding complement of $C_3$

Direct product of groups of homomorphisms

Abstract Algebra ( tutoring suggestions )

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

Application of First Fundamental theorem on Isomorphism.

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

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

Let $f:\mathbb{Z} \rightarrow \mathbb{Z}_{10}$ is homomorphism. Determine $f(18)$ such that $f(1)=6$.

General form of a group morphism $\tau : \mathbb{Z}_p \to \operatorname{Aut}(\mathbb{Z}_q)$ such that $\bar{k} \mapsto \tau_{\bar{k}}$

Compute the kernel of the group hom $\Omega : \Bbb{Q}^{\times} \to \Bbb{Z}^+$.

If $f:\mathbb{Z}\times \mathbb{Z} \rightarrow \mathbb{Z} \times \mathbb{Z}$ is homomorphism, show that $f$ is monomorphism.

Condition for triviality of group morphism $\tau : \mathbb{Z}_p \to\mathrm{Aut}(\mathbb{Z}_q)$ : $\tau_\overline{k}(\overline{n}) = \bar{r}^k \bar{n}$

How would I prove the following theorem on quaternions?

Homomorphic image of an alternating group

Proof: If $ϕ: R \to R'$ is a ring isomorphism, then its inverse $ϕ^{-1} : R' \to R$ is a ring homomorphism.

Trending Questions

Popular # Hahtags

Popular Questions