Question

Doubt regarding the identical nature of groups that are isomorphic.

score 76 · Answer 1 · 2021-10-19 08:57:37

76

Views

Doubt regarding the identical nature of groups that are isomorphic.

Published on 19 Oct 2021 - 8:57

score 86 · Answer 2 · 2026-03-29 08:20:59

86

Views

Determine whether $D_4/Z(D_4)\otimes Z(D_4)$ is isomorphic to $D_4$

Published on 29 Mar 2026 - 8:20

score 327 · Answer 3 · 2026-04-04 07:53:29

327

Views

Preimage of a homomorphism preserves the index?

Published on 04 Apr 2026 - 7:53

score 211 · Answer 4 · 2026-04-06 14:40:03

211

Views

Find the number of generators for $(\mu_{25}, .)$

Published on 06 Apr 2026 - 14:40

score 81 · Answer 5 · 2021-10-24 14:15:45

81

Views

How to find an isomorphism between two representations of $S3$ $(\Bbb{R}^2,\rho), (W_1(\subset\Bbb{R}^3),\pi)$?

Published on 24 Oct 2021 - 14:15

score 458 · Answer 6 · 2026-04-08 00:53:00

458

Views

Does the symmetric group $S_{n+m}$ have a subgroup isomorphic to $S_n\times S_m$?

Published on 08 Apr 2026 - 0:53

score 151 · Answer 7 · 2026-04-04 09:40:14

151

Views

How many homomorphisms are there from one group to another group?

Published on 04 Apr 2026 - 9:40

score 148 · Answer 8 · 2026-04-01 12:18:16

148

Views

Proving a group is abelian and of odd order?

Published on 01 Apr 2026 - 12:18

score 239 · Answer 9 · 2021-10-28 14:49:10

239

Views

To which well known group the quotient group $\mathbb R^/\mathbb{Q}^$ is isomorphic?

Published on 28 Oct 2021 - 14:49

score 68 · Answer 10 · 2026-04-04 09:43:17

68

Views

Let $t\in\Bbb N,t\ge 1,(G,+,0)$ abelian group $|G|=n$ and $\gcd(t,n)=1$ Prove $f(x)=tx$ is an automorphism

Published on 04 Apr 2026 - 9:43

score 77 · Answer 11 · 2026-04-01 12:15:26

77

Views

Prove $\phi:(\mathbb{Z}/n\mathbb{Z})^{\times}\to\text{Aut}(\mathbb{Z}_n)$ such that $[x]\mapsto \phi_{[x]}([t])=x[t]$ is an isomorphism

Published on 01 Apr 2026 - 12:15

score 110 · Answer 12 · 2021-11-01 15:10:55

110

Views

Group isomorphism from quotient ring $R/P$ to $P^n / P^{n+1}$

Published on 01 Nov 2021 - 15:10

score 46 · Answer 13 · 2021-11-07 06:33:42

46

Views

Prove that if $H \leq G, M \trianglelefteq G, M \leq H,$ and $xHx^{-1}/M =H/M$, then $xM \in N_G (H)/M$.

Published on 07 Nov 2021 - 6:33

score 46 · Answer 14 · 2026-04-04 09:36:31

46

Views

Strategies to find easy isomorphism between basics groups

Published on 04 Apr 2026 - 9:36

score 88 · Answer 15 · 2026-04-01 13:42:55

88

Views

If $\mathrm{Aut}(G \times H) \cong \mathrm{Aut}(G) \times \mathrm{Aut}(H)$, then is $\mathrm{gcd}(\left| G \right|, \left| H \right|) = 1$?

Published on 01 Apr 2026 - 13:42

List Question

Doubt regarding the identical nature of groups that are isomorphic.

Determine whether $D_4/Z(D_4)\otimes Z(D_4)$ is isomorphic to $D_4$

Preimage of a homomorphism preserves the index?

Find the number of generators for $(\mu_{25}, .)$

How to find an isomorphism between two representations of $S3$ $(\Bbb{R}^2,\rho), (W_1(\subset\Bbb{R}^3),\pi)$?

Does the symmetric group $S_{n+m}$ have a subgroup isomorphic to $S_n\times S_m$?

How many homomorphisms are there from one group to another group?

Proving a group is abelian and of odd order?

To which well known group the quotient group $\mathbb R^/\mathbb{Q}^$ is isomorphic?

Let $t\in\Bbb N,t\ge 1,(G,+,0)$ abelian group $|G|=n$ and $\gcd(t,n)=1$ Prove $f(x)=tx$ is an automorphism

Prove $\phi:(\mathbb{Z}/n\mathbb{Z})^{\times}\to\text{Aut}(\mathbb{Z}_n)$ such that $[x]\mapsto \phi_{[x]}([t])=x[t]$ is an isomorphism

Group isomorphism from quotient ring $R/P$ to $P^n / P^{n+1}$

Prove that if $H \leq G, M \trianglelefteq G, M \leq H,$ and $xHx^{-1}/M =H/M$, then $xM \in N_G (H)/M$.

Strategies to find easy isomorphism between basics groups

If $\mathrm{Aut}(G \times H) \cong \mathrm{Aut}(G) \times \mathrm{Aut}(H)$, then is $\mathrm{gcd}(\left| G \right|, \left| H \right|) = 1$?

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