Question

The multiplicative groups $\mathbb{Q}^\ast$ and $\mathbb{R}^\ast$ are not isomorphic

score 1.1k · Answer 1 · 2016-08-23 21:28:53

1.1k

Views

The multiplicative groups $\mathbb{Q}^\ast$ and $\mathbb{R}^\ast$ are not isomorphic

Published on 23 Aug 2016 - 21:28

score 4.4k · Answer 2 · 2016-08-25 01:09:07

4.4k

Views

Does any homomorphism map generators to generators?

Published on 25 Aug 2016 - 1:09

score 758 · Answer 3 · 2016-08-25 06:23:29

758

Views

Isomorphism $SU(2)/{\pm 1} \leftrightarrow SO(3)$

Published on 25 Aug 2016 - 6:23

score 95 · Answer 4 · 2016-08-27 02:09:01

95

Views

In Lang's "Algebra", p.56 line 5, what does that mean by "Two such isomorphims differ by an inner automorphism"?

Published on 27 Aug 2016 - 2:09

score 104 · Answer 5 · 2026-03-26 06:32:41

104

Views

$H,K$ be subgroups of an infinite abelian group $G$ such that $K \subseteq H$ and $G \cong K$ , then is it true that $G\cong H$ ?

Published on 26 Mar 2026 - 6:32

score 148 · Answer 6 · 2026-03-29 05:44:04

148

Views

$\operatorname{Hom}(G_1 \times ... \times G_k,G) \cong \operatorname{Hom}(G_1,G) \times....\times \mathrm{Hom}(G_k,G)$ where $G_i,G$ are groups?

Published on 29 Mar 2026 - 5:44

score 30 · Answer 7 · 2016-08-30 01:08:56

30

Views

Group Isomorphisms. Need clarification of question.

Published on 30 Aug 2016 - 1:08

score 57 · Answer 8 · 2016-08-31 11:48:39

57

Views

Show that the map $\phi : Z_{rs}\to Z_r\times\ Z_{s}$ defined by $\phi(m\cdot 1)=m(1,1)$ is surjective with $gcd(r,s)=1$.

Published on 31 Aug 2016 - 11:48

score 83 · Answer 9 · 2026-03-26 21:27:32

83

Views

I believe the following are isomorphic to $S_4$, how do I check?

Published on 26 Mar 2026 - 21:27

score 1.9k · Answer 10 · 2026-03-25 13:34:20

1.9k

Views

Does there exist a pair of infinite fields, the additive group of one isomorphic to the multiplicative group of the other?

Published on 25 Mar 2026 - 13:34

score 142 · Answer 11 · 2026-03-29 23:45:00

142

Views

Why $S_4 / V_4 \cong C_6 \Longleftrightarrow A_4 \leq V_4 $?

Published on 29 Mar 2026 - 23:45

score 691 · Answer 12 · 2016-09-12 06:20:40

691

Views

Cayley Tables and Isomorphisms

Published on 12 Sep 2016 - 6:20

score 782 · Answer 13 · 2026-03-29 04:10:54

782

Views

The symmetric group of $\mathbb{Z}$ is isomorphic to which group?

Published on 29 Mar 2026 - 4:10

score 55 · Answer 14 · 2016-09-16 15:16:32

55

Views

Validating and proving a property of Group Isomorphism

Published on 16 Sep 2016 - 15:16

score 172 · Answer 15 · 2016-09-21 20:04:18

172

Views

Permutation group isomorphism

Published on 21 Sep 2016 - 20:04

List Question

The multiplicative groups $\mathbb{Q}^\ast$ and $\mathbb{R}^\ast$ are not isomorphic

Does any homomorphism map generators to generators?

Isomorphism $SU(2)/{\pm 1} \leftrightarrow SO(3)$

In Lang's "Algebra", p.56 line 5, what does that mean by "Two such isomorphims differ by an inner automorphism"?

$H,K$ be subgroups of an infinite abelian group $G$ such that $K \subseteq H$ and $G \cong K$ , then is it true that $G\cong H$ ?

$\operatorname{Hom}(G_1 \times ... \times G_k,G) \cong \operatorname{Hom}(G_1,G) \times....\times \mathrm{Hom}(G_k,G)$ where $G_i,G$ are groups?

Group Isomorphisms. Need clarification of question.

Show that the map $\phi : Z_{rs}\to Z_r\times\ Z_{s}$ defined by $\phi(m\cdot 1)=m(1,1)$ is surjective with $gcd(r,s)=1$.

I believe the following are isomorphic to $S_4$, how do I check?

Does there exist a pair of infinite fields, the additive group of one isomorphic to the multiplicative group of the other?

Why $S_4 / V_4 \cong C_6 \Longleftrightarrow A_4 \leq V_4 $?

Cayley Tables and Isomorphisms

The symmetric group of $\mathbb{Z}$ is isomorphic to which group?

Validating and proving a property of Group Isomorphism

Permutation group isomorphism

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