Question

Isomorphism normal quotient subgroups

score 57 · Answer 1 · 2026-04-16 11:04:15

57

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Isomorphism normal quotient subgroups

Published on 16 Apr 2026 - 11:04

score 3.3k · Answer 2 · 2026-04-17 07:01:04

3.3k

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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 17 Apr 2026 - 7:01

score 284 · Answer 3 · 2026-04-10 21:29:06

284

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Proving an isomorphism using the isomorphism theorems

Published on 10 Apr 2026 - 21:29

score 2.4k · Answer 4 · 2026-05-10 16:06:20

2.4k

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

Published on 10 May 2026 - 16:06

score 306 · Answer 5 · 2026-04-13 20:54:54

306

Views

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

Published on 13 Apr 2026 - 20:54

score 113 · Answer 6 · 2026-04-14 08:09:47

113

Views

Formal way of writing an isomorphism between unitriangular matrix groups

Published on 14 Apr 2026 - 8:09

score 1.3k · Answer 7 · 2026-05-10 17:17:30

1.3k

Views

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

Published on 10 May 2026 - 17:17

score 723 · Answer 8 · 2026-04-12 17:03:36

723

Views

Cayley’s Theorem Isomorphic Subgroup

Published on 12 Apr 2026 - 17:03

score 127 · Answer 9 · 2026-05-10 19:51:43

127

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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 10 May 2026 - 19:51

score 303 · Answer 10 · 2026-04-12 05:20:46

303

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About Groups and Isomorphic Quotients

Published on 12 Apr 2026 - 5:20

score 108 · Answer 11 · 2026-04-15 13:48:56

108

Views

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

Published on 15 Apr 2026 - 13:48

score 39 · Answer 12 · 2026-04-14 17:08:29

39

Views

Showing isomorphism between two groups (true or false question)

Published on 14 Apr 2026 - 17:08

score 65 · Answer 13 · 2026-04-14 18:51:34

65

Views

$Z_5$ isomorphic to a subgroup of $S_4$

Published on 14 Apr 2026 - 18:51

score 103 · Answer 14 · 2026-04-13 10:56:31

103

Views

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

Published on 13 Apr 2026 - 10:56

score 573 · Answer 15 · 2026-04-14 20:31:23

573

Views

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

Published on 14 Apr 2026 - 20:31

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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