Question

In $(G_1\times G_2)/G_2$, I am confused since $G_2$ is clearly not a subgroup of $G_1\times G_2$

score 93 · Answer 1 · 2023-12-10 06:13:41

93

Views

In $(G_1\times G_2)/G_2$, I am confused since $G_2$ is clearly not a subgroup of $G_1\times G_2$

Published on 10 Dec 2023 - 6:13

score 546 · Answer 2 · 2023-12-16 18:53:23

546

Views

Does $\mathbb{R}/\mathbb{Q}$ contain a subgroup isomorphic to $\mathbb{Q}$?

Published on 16 Dec 2023 - 18:53

score 99 · Answer 3 · 2026-03-27 00:58:42

99

Views

Elements of $\mathbb{Z}/p\mathbb{Z}$ and prove it's simple group

Published on 27 Mar 2026 - 0:58

score 69 · Answer 4 · 2024-01-09 12:39:35

69

Views

Showing that a normal subgroup is equal to the kernel of a homomorphism.

Published on 09 Jan 2024 - 12:39

score 73 · Answer 5 · 2024-01-18 10:17:33

73

Views

If $G \cong G'$ and $H \cong H'$ where $H \trianglelefteq G$ and $H' \trianglelefteq G'$, is then also $G/H \cong G'/H'$?

Published on 18 Jan 2024 - 10:17

score 56 · Answer 6 · 2026-03-26 19:00:58

56

Views

Let $K\le H\le G$ with $[G:H]<\infty$. Is $[G:K]<\infty$ necessarily?

Published on 26 Mar 2026 - 19:00

score 63 · Answer 7 · 2024-01-26 10:55:10

63

Views

Example for $[G : G\cap H] \neq [H:G\cap H]$ with isomorphic subgroups $G \cong H$?

Published on 26 Jan 2024 - 10:55

score 36 · Answer 8 · 2024-01-28 19:34:14

36

Views

Rules of Products of Quotient Groups

Published on 28 Jan 2024 - 19:34

score 71 · Answer 9 · 2024-02-03 03:45:59

71

Views

Let $R$ be a P.I.D. and let $a \neq 0$ be an element in $R$. Prove that for a prime element $p$, $p(R/(a)) = ((p) + (a))/(a)$.

Published on 03 Feb 2024 - 3:45

score 84 · Answer 10 · 2026-03-25 22:10:43

84

Views

Prove that $\mathbb{R}[x]/(x^2+1)^2$ is isomorphic to $\mathbb{C}[y]/(y^2)$ as a $\mathbb{C}$-algebra.

Published on 25 Mar 2026 - 22:10

score 41 · Answer 11 · 2026-03-26 08:04:32

41

Views

Subgroups and Quotient Groups of Infinite bounded Abelian p-groups

Published on 26 Mar 2026 - 8:04

score 77 · Answer 12 · 2024-02-21 17:05:46

77

Views

Decomposition of $z^q-z$ with $q=p^n$ in $\mathbb{K}[x]$ with $|\mathbb{K}|=q$.

Published on 21 Feb 2024 - 17:05

score 40 · Answer 13 · 2026-03-25 01:26:01

40

Views

Ordering of group elements in MultiplicationTable vs CosetTable in GAP

Published on 25 Mar 2026 - 1:26

score 15.6k · Answer 14 · 2015-05-20 03:13:00

15.6k

Views

If $G$ is cyclic then $G/H$ is cyclic?

Published on 20 May 2015 - 3:13

score 1.8k · Answer 15 · 2015-05-23 02:22:15

1.8k

Views

Complex numbers modulo integers

Published on 23 May 2015 - 2:22

List Question

In $(G_1\times G_2)/G_2$, I am confused since $G_2$ is clearly not a subgroup of $G_1\times G_2$

Does $\mathbb{R}/\mathbb{Q}$ contain a subgroup isomorphic to $\mathbb{Q}$?

Elements of $\mathbb{Z}/p\mathbb{Z}$ and prove it's simple group

Showing that a normal subgroup is equal to the kernel of a homomorphism.

If $G \cong G'$ and $H \cong H'$ where $H \trianglelefteq G$ and $H' \trianglelefteq G'$, is then also $G/H \cong G'/H'$?

Let $K\le H\le G$ with $[G:H]<\infty$. Is $[G:K]<\infty$ necessarily?

Example for $[G : G\cap H] \neq [H:G\cap H]$ with isomorphic subgroups $G \cong H$?

Rules of Products of Quotient Groups

Let $R$ be a P.I.D. and let $a \neq 0$ be an element in $R$. Prove that for a prime element $p$, $p(R/(a)) = ((p) + (a))/(a)$.

Prove that $\mathbb{R}[x]/(x^2+1)^2$ is isomorphic to $\mathbb{C}[y]/(y^2)$ as a $\mathbb{C}$-algebra.

Subgroups and Quotient Groups of Infinite bounded Abelian p-groups

Decomposition of $z^q-z$ with $q=p^n$ in $\mathbb{K}[x]$ with $|\mathbb{K}|=q$.

Ordering of group elements in MultiplicationTable vs CosetTable in GAP

If $G$ is cyclic then $G/H$ is cyclic?

Complex numbers modulo integers

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