Question

Non-abelian Order of $6$ is isomorphic to $S_3$

score 108 · Answer 1 · 2016-07-23 19:18:37

108

Views

Non-abelian Order of $6$ is isomorphic to $S_3$

Published on 23 Jul 2016 - 19:18

score 2.2k · Answer 2 · 2016-07-24 15:58:43

2.2k

Views

$\mathbb{C}/\mathbb{Z}$ is isomorphic to multiplicative group $\mathbb{C}\setminus\{0\}$

Published on 24 Jul 2016 - 15:58

score 387 · Answer 3 · 2016-07-24 16:45:43

387

Views

If $f \otimes \text{id}_{\Bbb Q}$ and $f \otimes \text{id}_{\Bbb{F}_p}$ are isomorphisms, is $f$ an isomorphism?

Published on 24 Jul 2016 - 16:45

score 675 · Answer 4 · 2026-03-25 11:54:19

675

Views

Let $R$ be a commutative unital ring. Is it true that the group of units of $R$ is not isomorphic with the additive group of $R$?

Published on 25 Mar 2026 - 11:54

score 257 · Answer 5 · 2026-03-26 06:01:36

257

Views

If $R$ is a commutative unital ring with no non-trivial idempotents, then is the group of units of $R$ not isomorphic with the additive group of $R$?

Published on 26 Mar 2026 - 6:01

score 239 · Answer 6 · 2016-07-28 06:43:56

239

Views

Retractions and Isomorphisms of Fundamental Groups

Published on 28 Jul 2016 - 6:43

score 167 · Answer 7 · 2026-03-26 19:20:13

167

Views

Geometrical Interpretation of quotient group of $D_{n}$ being isomorphic to $\{1,-1\} $

Published on 26 Mar 2026 - 19:20

score 3.9k · Answer 8 · 2016-08-02 09:10:45

3.9k

Views

Isomorphisms preserve cyclic

Published on 02 Aug 2016 - 9:10

score 841 · Answer 9 · 2016-08-03 00:09:30

841

Views

The number of isomorphisms from $\mathbb{Z}_{12}$ to itself is 4.

Published on 03 Aug 2016 - 0:09

score 389 · Answer 10 · 2016-08-03 16:11:36

389

Views

If $G\simeq K$ and $H\simeq M$ then is it true that $G/ H \simeq K / M$?

Published on 03 Aug 2016 - 16:11

score 512 · Answer 11 · 2016-08-04 15:05:57

512

Views

Is $gG$ equal to $G$ or is $gG$ isomorphic to $G$?

Published on 04 Aug 2016 - 15:05

score 1.9k · Answer 12 · 2026-03-27 23:06:06

1.9k

Views

Seeing $PSL_2(\mathbb{C}) \cong SO_3(\mathbb{C})$

Published on 27 Mar 2026 - 23:06

score 390 · Answer 13 · 2026-03-26 04:52:06

390

Views

Is $(\mathbb Q^+, . )$ isomorphic with a subgroup of $(\mathbb R,+)$ ?

Published on 26 Mar 2026 - 4:52

score 1.8k · Answer 14 · 2016-08-21 17:27:52

1.8k

Views

Constructing groups of order 16 from knowledge of their subgroups

Published on 21 Aug 2016 - 17:27

score 407 · Answer 15 · 2026-03-26 17:32:15

407

Views

A characteristic subgroup of the free group $F_2$

Published on 26 Mar 2026 - 17:32

List Question

Non-abelian Order of $6$ is isomorphic to $S_3$

$\mathbb{C}/\mathbb{Z}$ is isomorphic to multiplicative group $\mathbb{C}\setminus\{0\}$

If $f \otimes \text{id}_{\Bbb Q}$ and $f \otimes \text{id}_{\Bbb{F}_p}$ are isomorphisms, is $f$ an isomorphism?

Let $R$ be a commutative unital ring. Is it true that the group of units of $R$ is not isomorphic with the additive group of $R$?

If $R$ is a commutative unital ring with no non-trivial idempotents, then is the group of units of $R$ not isomorphic with the additive group of $R$?

Retractions and Isomorphisms of Fundamental Groups

Geometrical Interpretation of quotient group of $D_{n}$ being isomorphic to $\{1,-1\} $

Isomorphisms preserve cyclic

The number of isomorphisms from $\mathbb{Z}_{12}$ to itself is 4.

If $G\simeq K$ and $H\simeq M$ then is it true that $G/ H \simeq K / M$?

Is $gG$ equal to $G$ or is $gG$ isomorphic to $G$?

Seeing $PSL_2(\mathbb{C}) \cong SO_3(\mathbb{C})$

Is $(\mathbb Q^+, . )$ isomorphic with a subgroup of $(\mathbb R,+)$ ?

Constructing groups of order 16 from knowledge of their subgroups

A characteristic subgroup of the free group $F_2$

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