Question

$G=(\mathbb{R}^*,\cdot)$ , $N=\{-1,1\}$. prove that $G/N\cong (\mathbb{R}_+,\cdot)$

score 37 · Answer 1 · 2015-06-07 19:48:58

37

Views

$G=(\mathbb{R}^*,\cdot)$ , $N=\{-1,1\}$. prove that $G/N\cong (\mathbb{R}_+,\cdot)$

Published on 07 Jun 2015 - 19:48

score 52 · Answer 2 · 2015-06-08 10:22:07

52

Views

Is there any group $G$ with $ord(G)=20$ so that $\varphi:G\rightarrow \mathbb{Z}_{10}$ is epimorphism?

Published on 08 Jun 2015 - 10:22

score 61 · Answer 3 · 2015-06-08 17:50:57

61

Views

Is there any group $G$ with $ord(G)=20$ so that $\varphi:G\rightarrow \mathbb{Z}_{15}$ is epimorphism?

Published on 08 Jun 2015 - 17:50

score 577 · Answer 4 · 2015-06-10 13:51:48

577

Views

Prove that all normal subgroup definitions are equivalent.

Published on 10 Jun 2015 - 13:51

score 73 · Answer 5 · 2015-06-11 13:00:31

73

Views

Grupoids - congruencies and homomorphisms

Published on 11 Jun 2015 - 13:00

score 52 · Answer 6 · 2015-06-14 20:30:48

52

Views

prove that $\Bbb Z/n \Bbb Z \cong \mu_n$

Published on 14 Jun 2015 - 20:30

score 157 · Answer 7 · 2026-03-28 11:54:15

157

Views

Why is $\operatorname{Hom}_{\mathrm{Groups}}(G,A)$ isomorphic to $\operatorname{Hom}_{\mathrm{Ab}}(G/[G,G],A)$?

Published on 28 Mar 2026 - 11:54

score 369 · Answer 8 · 2015-06-16 13:50:29

369

Views

Group homomorphism identify kernel

Published on 16 Jun 2015 - 13:50

score 193 · Answer 9 · 2015-06-16 22:13:50

193

Views

Induced homomorphism $\phi^*$ from $G/M \to H/N\ ?$

Published on 16 Jun 2015 - 22:13

score 128 · Answer 10 · 2015-06-17 17:28:37

128

Views

What are the groups $\text{Hom}(F^\times\!, F^+\!)$ and $\text{Hom}(F^+\!, F^\times\!)$?

Published on 17 Jun 2015 - 17:28

score 796 · Answer 11 · 2015-06-18 21:53:37

796

Views

Is an injective morphism from a Lie group to itself surjective?

Published on 18 Jun 2015 - 21:53

score 77 · Answer 12 · 2015-06-20 17:26:40

77

Views

Prove that: $B/A \triangleleft R/A$ if $A \subseteq B ;\ \ A, B \triangleleft R $(ring)

Published on 20 Jun 2015 - 17:26

score 1.4k · Answer 13 · 2015-06-22 13:01:46

1.4k

Views

Is this a homomorphism? Matrix homomorphism $\phi:\Bbb R\to GL_2(\Bbb R)$

Published on 22 Jun 2015 - 13:01

score 3k · Answer 14 · 2015-06-24 15:47:40

3k

Views

How to determine non trivial homomorphisms

Published on 24 Jun 2015 - 15:47

score 158 · Answer 15 · 2026-02-23 04:33:47

158

Views

LCA - groups under continuous homomorphisms

Published on 23 Feb 2026 - 4:33

List Question

$G=(\mathbb{R}^*,\cdot)$ , $N=\{-1,1\}$. prove that $G/N\cong (\mathbb{R}_+,\cdot)$

Is there any group $G$ with $ord(G)=20$ so that $\varphi:G\rightarrow \mathbb{Z}_{10}$ is epimorphism?

Is there any group $G$ with $ord(G)=20$ so that $\varphi:G\rightarrow \mathbb{Z}_{15}$ is epimorphism?

Prove that all normal subgroup definitions are equivalent.

Grupoids - congruencies and homomorphisms

prove that $\Bbb Z/n \Bbb Z \cong \mu_n$

Why is $\operatorname{Hom}_{\mathrm{Groups}}(G,A)$ isomorphic to $\operatorname{Hom}_{\mathrm{Ab}}(G/[G,G],A)$?

Group homomorphism identify kernel

Induced homomorphism $\phi^*$ from $G/M \to H/N\ ?$

What are the groups $\text{Hom}(F^\times\!, F^+\!)$ and $\text{Hom}(F^+\!, F^\times\!)$?

Is an injective morphism from a Lie group to itself surjective?

Prove that: $B/A \triangleleft R/A$ if $A \subseteq B ;\ \ A, B \triangleleft R $(ring)

Is this a homomorphism? Matrix homomorphism $\phi:\Bbb R\to GL_2(\Bbb R)$

How to determine non trivial homomorphisms

LCA - groups under continuous homomorphisms

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