Question

Isomorphism normal quotient subgroups

score 54 · Answer 1 · 2018-05-03 14:29:05

54

Views

Isomorphism normal quotient subgroups

Published on 03 May 2018 - 14:29

score 3.3k · Answer 2 · 2018-05-03 14:41:10

3.3k

Views

Let m, n be positive integers. Show that Zmn and Zm × Zn are isomorphic if and only if m and n are coprime (i.e. gcd(m, n) = 1).

Published on 03 May 2018 - 14:41

score 281 · Answer 3 · 2018-05-03 14:44:13

281

Views

Proving an isomorphism using the isomorphism theorems

Published on 03 May 2018 - 14:44

score 2.4k · Answer 4 · 2026-03-25 07:45:21

2.4k

Views

Is $G$ isomorphic to $\frac{G}{H}\times H$?

Published on 25 Mar 2026 - 7:45

score 304 · Answer 5 · 2026-03-26 12:07:41

304

Views

If $G\times K\cong H\times K$, is $G\cong H$?

Published on 26 Mar 2026 - 12:07

score 110 · Answer 6 · 2018-05-06 21:49:38

110

Views

Formal way of writing an isomorphism between unitriangular matrix groups

Published on 06 May 2018 - 21:49

score 1.3k · Answer 7 · 2026-03-25 09:28:58

1.3k

Views

Prove that, $\operatorname{Aut}(S_3)\simeq S_3 \simeq \operatorname{Inn}(S_3)$

Published on 25 Mar 2026 - 9:28

score 720 · Answer 8 · 2018-05-08 12:03:33

720

Views

Cayley’s Theorem Isomorphic Subgroup

Published on 08 May 2018 - 12:03

score 124 · Answer 9 · 2026-03-26 02:47:53

124

Views

Prove $\langle k \rangle / \langle km \rangle \simeq \mathbb {Z}_m,$ where $\langle k \rangle$ is the subgroup generated by $k$ and $k\in \mathbb{Z}$

Published on 26 Mar 2026 - 2:47

score 300 · Answer 10 · 2018-05-10 20:49:00

300

Views

About Groups and Isomorphic Quotients

Published on 10 May 2018 - 20:49

score 105 · Answer 11 · 2018-05-10 23:30:09

105

Views

Is there a subgroup of $S_7$ that's isomorphic to $\Bbb Z_2\times \Bbb Z_4$?

Published on 10 May 2018 - 23:30

score 36 · Answer 12 · 2018-05-10 23:35:33

36

Views

Showing isomorphism between two groups (true or false question)

Published on 10 May 2018 - 23:35

score 62 · Answer 13 · 2018-05-10 23:54:03

62

Views

$Z_5$ isomorphic to a subgroup of $S_4$

Published on 10 May 2018 - 23:54

score 100 · Answer 14 · 2018-05-12 19:19:25

100

Views

Why do the steps in this proof to show that $\theta(e_1)=e_2$ for a group isomorphism make sense?

Published on 12 May 2018 - 19:19

score 571 · Answer 15 · 2026-03-26 15:17:10

571

Views

Proving a finite group is isomorphic to $(\Bbb Z/2)^n$

Published on 26 Mar 2026 - 15:17

List Question

Isomorphism normal quotient subgroups

Let m, n be positive integers. Show that Zmn and Zm × Zn are isomorphic if and only if m and n are coprime (i.e. gcd(m, n) = 1).

Proving an isomorphism using the isomorphism theorems

Is $G$ isomorphic to $\frac{G}{H}\times H$?

If $G\times K\cong H\times K$, is $G\cong H$?

Formal way of writing an isomorphism between unitriangular matrix groups

Prove that, $\operatorname{Aut}(S_3)\simeq S_3 \simeq \operatorname{Inn}(S_3)$

Cayley’s Theorem Isomorphic Subgroup

Prove $\langle k \rangle / \langle km \rangle \simeq \mathbb {Z}_m,$ where $\langle k \rangle$ is the subgroup generated by $k$ and $k\in \mathbb{Z}$

About Groups and Isomorphic Quotients

Is there a subgroup of $S_7$ that's isomorphic to $\Bbb Z_2\times \Bbb Z_4$?

Showing isomorphism between two groups (true or false question)

$Z_5$ isomorphic to a subgroup of $S_4$

Why do the steps in this proof to show that $\theta(e_1)=e_2$ for a group isomorphism make sense?

Proving a finite group is isomorphic to $(\Bbb Z/2)^n$

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