Question

Classifying groups of order $8$

score 140 · Answer 1 · 2026-04-01 14:21:00

140

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Classifying groups of order $8$

Published on 01 Apr 2026 - 14:21

score 631 · Answer 2 · 2015-02-17 02:02:01

631

Views

Find a group that the additive group $\mathbb{R} / \mathbb{Z}$ is isomorphic to

Published on 17 Feb 2015 - 2:02

score 335 · Answer 3 · 2015-02-18 12:49:42

335

Views

How do I prove $\mathbb{Z}\times\mathbb{Z}\times\mathbb{Z}$ and $\mathbb{Z}\times\mathbb{Z}$ are not isomorphic?

Published on 18 Feb 2015 - 12:49

score 321 · Answer 4 · 2015-02-18 16:26:28

321

Views

Let $\varphi:G\to K$ be homomorphism, where $G$ is a finite group and $K$,arbitrary group. Suppose $H$ be a subgroup of $G$ Prove the following:

Published on 18 Feb 2015 - 16:26

score 87 · Answer 5 · 2015-02-19 13:56:01

87

Views

Why homomorph and not isomorph?

Published on 19 Feb 2015 - 13:56

score 1.9k · Answer 6 · 2015-02-20 04:53:28

1.9k

Views

If there is a bijection $f: X\rightarrow Y$, prove that there exists an isomorphism $\phi :S_X\rightarrow S_Y$

Published on 20 Feb 2015 - 4:53

score 481 · Answer 7 · 2026-03-27 02:36:06

481

Views

Show $S_n$ contains a subgroup isomorphic to direct product of $S_{n_1}, ..., S_{n_k}$...

Published on 27 Mar 2026 - 2:36

score 78 · Answer 8 · 2015-02-27 16:37:34

78

Views

Homomorphism and images

Published on 27 Feb 2015 - 16:37

score 329 · Answer 9 · 2026-04-03 06:14:29

329

Views

Can we describe all group isomorphisms from $(\mathbb R ,+)$ to $(\mathbb R^+ , .)$ ?

Published on 03 Apr 2026 - 6:14

score 133 · Answer 10 · 2015-03-04 09:04:28

133

Views

isomorphism argument

Published on 04 Mar 2015 - 9:04

score 1.5k · Answer 11 · 2026-03-27 04:17:03

1.5k

Views

Showing two groups are not isomorphic using the order of their elements.

Published on 27 Mar 2026 - 4:17

score 435 · Answer 12 · 2015-03-15 00:20:33

435

Views

Floor Function Homomorphism and Isomorphism

Published on 15 Mar 2015 - 0:20

score 165 · Answer 13 · 2015-03-16 22:14:25

165

Views

Why is $\mathbb{Z}_4 \times \mathbb{Z}_4 \times \mathbb{Z}_8 /\left<(1,2,4)\right>$ isomorphic to $\mathbb{Z}_4 \times \mathbb{Z}_8$?

Published on 16 Mar 2015 - 22:14

score 5.7k · Answer 14 · 2015-03-16 23:10:45

5.7k

Views

An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$

Published on 16 Mar 2015 - 23:10

score 112 · Answer 15 · 2015-03-18 00:58:04

112

Views

Find a subgroup of $S_{4}$ which is isomorphic to $\mathrm{Aut}(U_{8})$

Published on 18 Mar 2015 - 0:58

List Question

Classifying groups of order $8$

Find a group that the additive group $\mathbb{R} / \mathbb{Z}$ is isomorphic to

How do I prove $\mathbb{Z}\times\mathbb{Z}\times\mathbb{Z}$ and $\mathbb{Z}\times\mathbb{Z}$ are not isomorphic?

Let $\varphi:G\to K$ be homomorphism, where $G$ is a finite group and $K$,arbitrary group. Suppose $H$ be a subgroup of $G$ Prove the following:

Why homomorph and not isomorph?

If there is a bijection $f: X\rightarrow Y$, prove that there exists an isomorphism $\phi :S_X\rightarrow S_Y$

Show $S_n$ contains a subgroup isomorphic to direct product of $S_{n_1}, ..., S_{n_k}$...

Homomorphism and images

Can we describe all group isomorphisms from $(\mathbb R ,+)$ to $(\mathbb R^+ , .)$ ?

isomorphism argument

Showing two groups are not isomorphic using the order of their elements.

Floor Function Homomorphism and Isomorphism

Why is $\mathbb{Z}_4 \times \mathbb{Z}_4 \times \mathbb{Z}_8 /\left<(1,2,4)\right>$ isomorphic to $\mathbb{Z}_4 \times \mathbb{Z}_8$?

An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$

Find a subgroup of $S_{4}$ which is isomorphic to $\mathrm{Aut}(U_{8})$

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