Question

Mistake in my Second Isomorphism Theorem example

score 43 · Answer 1 · 2026-03-29 05:34:18

43

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Mistake in my Second Isomorphism Theorem example

Published on 29 Mar 2026 - 5:34

score 180 · Answer 2 · 2026-03-27 06:07:49

180

Views

Showing that $\mathbb{Z}_{24}$ is not isomorphic to $\mathbb{Z}_{4}\times\mathbb{Z}_6$

Published on 27 Mar 2026 - 6:07

score 224 · Answer 3 · 2026-03-29 11:49:53

224

Views

Showing ${\rm Aut}(D_{2^n})\cong{\rm Aut}(Q_{2^n})$ for $n\ge 4$.

Published on 29 Mar 2026 - 11:49

score 90 · Answer 4 · 2022-01-01 20:12:37

90

Views

Prove this isomorphism about semidirect product $((\oplus_1^k \mathbb{Z}/2) \oplus \mathbb{Z}/n) \rtimes_{\varphi} \mathbb{Z}/2$.

Published on 01 Jan 2022 - 20:12

score 657 · Answer 5 · 2026-02-23 00:30:32

657

Views

Showing ${\rm Aut}(Q_{2^n})\cong{\rm Hol}(\Bbb Z_{2^{n-1}})$ for $n>3$

Published on 23 Feb 2026 - 0:30

score 213 · Answer 6 · 2026-03-28 20:14:28

213

Views

Is the given condition necessary for $HK$ to be isomorphic to $H\times K$?

Published on 28 Mar 2026 - 20:14

score 60 · Answer 7 · 2026-03-28 20:13:36

60

Views

Define a binary operation on {e,(12)}×{e,(123),(132)} so that it becomes isomorphic to $S_3$

Published on 28 Mar 2026 - 20:13

score 54 · Answer 8 · 2026-04-04 16:52:10

54

Views

What Should the Formula for this Map Be?

Published on 04 Apr 2026 - 16:52

score 38 · Answer 9 · 2026-04-08 07:32:16

38

Views

For a finite $G$ group and $f_g(x) = gx$, if the permutation $\pi(f_g)$ defines the values of $f_g$, then is $\pi(f_{gh})=\pi(f_g)\pi(f_h)$?

Published on 08 Apr 2026 - 7:32

score 32 · Answer 10 · 2026-04-08 16:32:36

32

Views

Finding the inverse of a group isomorphism linked to a short exact sequence

Published on 08 Apr 2026 - 16:32

score 58 · Answer 11 · 2022-01-29 08:08:55

58

Views

Why $\text{I}(\mathbb{R}^n)$ is not isomorphic to $\text{O}(n) \times \mathbb{R}^n$?

Published on 29 Jan 2022 - 8:08

score 41 · Answer 12 · 2026-04-01 10:00:27

41

Views

What are the values of $g$ on $(0,1)$ and $(1,0)$?

Published on 01 Apr 2026 - 10:00

score 578 · Answer 13 · 2026-04-06 21:11:35

578

Views

Prove that $\mathbb{Z} \times\Bbb Z_2$ and $\mathbb{Z}$ are not isomorphic.

Published on 06 Apr 2026 - 21:11

score 153 · Answer 14 · 2022-02-01 20:31:52

153

Views

If $\varphi: G \to H$ is an isomorphism and $N \trianglelefteq G$, then, $\varphi(N) \subseteq K$, where $K$ is some normal subgroup in $H$?

Published on 01 Feb 2022 - 20:31

score 279 · Answer 15 · 2022-02-03 08:22:29

279

Views

Proving that SO(3) is not isomorphic to another group

Published on 03 Feb 2022 - 8:22

List Question

Mistake in my Second Isomorphism Theorem example

Showing that $\mathbb{Z}_{24}$ is not isomorphic to $\mathbb{Z}_{4}\times\mathbb{Z}_6$

Showing ${\rm Aut}(D_{2^n})\cong{\rm Aut}(Q_{2^n})$ for $n\ge 4$.

Prove this isomorphism about semidirect product $((\oplus_1^k \mathbb{Z}/2) \oplus \mathbb{Z}/n) \rtimes_{\varphi} \mathbb{Z}/2$.

Showing ${\rm Aut}(Q_{2^n})\cong{\rm Hol}(\Bbb Z_{2^{n-1}})$ for $n>3$

Is the given condition necessary for $HK$ to be isomorphic to $H\times K$?

Define a binary operation on {e,(12)}×{e,(123),(132)} so that it becomes isomorphic to $S_3$

What Should the Formula for this Map Be?

For a finite $G$ group and $f_g(x) = gx$, if the permutation $\pi(f_g)$ defines the values of $f_g$, then is $\pi(f_{gh})=\pi(f_g)\pi(f_h)$?

Finding the inverse of a group isomorphism linked to a short exact sequence

Why $\text{I}(\mathbb{R}^n)$ is not isomorphic to $\text{O}(n) \times \mathbb{R}^n$?

What are the values of $g$ on $(0,1)$ and $(1,0)$?

Prove that $\mathbb{Z} \times\Bbb Z_2$ and $\mathbb{Z}$ are not isomorphic.

If $\varphi: G \to H$ is an isomorphism and $N \trianglelefteq G$, then, $\varphi(N) \subseteq K$, where $K$ is some normal subgroup in $H$?

Proving that SO(3) is not isomorphic to another group

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