Question

Example of $2$ non-isomorphic groups that have the same quotients

score 1.1k · Answer 1 · 2017-03-04 09:20:59

1.1k

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Example of $2$ non-isomorphic groups that have the same quotients

Published on 04 Mar 2017 - 9:20

score 70 · Answer 2 · 2017-03-05 19:39:42

70

Views

Unnecessary Steps in A Proof?

Published on 05 Mar 2017 - 19:39

score 90 · Answer 3 · 2017-03-06 20:21:20

90

Views

Show that $\varphi:\mathbb{R}→Gl_2 (\mathbb{R})$ defined by $\varphi(a)=\begin{pmatrix} 1 & a \\ 0 & 1\end{pmatrix}$ is not an isomorphism

Published on 06 Mar 2017 - 20:21

score 295 · Answer 4 · 2017-03-07 09:30:38

295

Views

Use the first isomorphism theorem to show two groups are isomorphic

Published on 07 Mar 2017 - 9:30

score 56 · Answer 5 · 2017-03-08 16:05:42

56

Views

Showing a ring with 1 is isomorphic to the ring of residue classes modulo p

Published on 08 Mar 2017 - 16:05

score 306 · Answer 6 · 2017-03-13 07:17:28

306

Views

Using the first isomorphism theorem

Published on 13 Mar 2017 - 7:17

score 249 · Answer 7 · 2026-03-30 16:46:20

249

Views

How to geometrically show that there are $4$ $S_3$ subgroups in $S_4$?

Published on 30 Mar 2026 - 16:46

score 267 · Answer 8 · 2017-03-13 13:45:03

267

Views

Showing Aut of G is a group

Published on 13 Mar 2017 - 13:45

score 88 · Answer 9 · 2017-03-14 14:07:03

88

Views

Confusion about the classification of groups of order $8$

Published on 14 Mar 2017 - 14:07

score 412 · Answer 10 · 2026-03-27 22:15:09

412

Views

For finitely generated abelian groups $A$ and $B$, prove that $A \oplus A \simeq B \oplus B$ implies $A \simeq B$

Published on 27 Mar 2026 - 22:15

score 139 · Answer 11 · 2017-03-16 16:48:49

139

Views

Well-known isomorphism

Published on 16 Mar 2017 - 16:48

score 2k · Answer 12 · 2026-03-29 20:55:58

2k

Views

Finding the kernel of $\phi$ of applying the First Isomorphism Theorem

Published on 29 Mar 2026 - 20:55

score 1.7k · Answer 13 · 2026-03-28 14:06:32

1.7k

Views

Group of units of direct sum of rings is isomorphic to direct sum of the groups of units

Published on 28 Mar 2026 - 14:06

score 325 · Answer 14 · 2017-03-20 01:10:20

325

Views

Finding cosets in a quotient group and verify that they are isomorphic to each other

Published on 20 Mar 2017 - 1:10

score 1.1k · Answer 15 · 2026-03-31 12:44:32

1.1k

Views

Prove that all cyclic groups of the same order are isomorphic

Published on 31 Mar 2026 - 12:44

List Question

Example of $2$ non-isomorphic groups that have the same quotients

Unnecessary Steps in A Proof?

Show that $\varphi:\mathbb{R}→Gl_2 (\mathbb{R})$ defined by $\varphi(a)=\begin{pmatrix} 1 & a \\ 0 & 1\end{pmatrix}$ is not an isomorphism

Use the first isomorphism theorem to show two groups are isomorphic

Showing a ring with 1 is isomorphic to the ring of residue classes modulo p

Using the first isomorphism theorem

How to geometrically show that there are $4$ $S_3$ subgroups in $S_4$?

Showing Aut of G is a group

Confusion about the classification of groups of order $8$

For finitely generated abelian groups $A$ and $B$, prove that $A \oplus A \simeq B \oplus B$ implies $A \simeq B$

Well-known isomorphism

Finding the kernel of $\phi$ of applying the First Isomorphism Theorem

Group of units of direct sum of rings is isomorphic to direct sum of the groups of units

Finding cosets in a quotient group and verify that they are isomorphic to each other

Prove that all cyclic groups of the same order are isomorphic

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