Question

Solvable normal subgroup but the corresponding quotient group is not solvable

score 71 · Answer 1 · 2026-03-28 12:03:02

71

Views

Solvable normal subgroup but the corresponding quotient group is not solvable

Published on 28 Mar 2026 - 12:03

score 58 · Answer 2 · 2026-02-23 20:40:56

58

Views

Prove or give counter example: $G \cong N \times G/N \Rightarrow N$ has a normal complement.

Published on 23 Feb 2026 - 20:40

score 87 · Answer 3 · 2026-03-26 11:05:00

87

Views

Nilpotent of subgroup implies nilpotent of group

Published on 26 Mar 2026 - 11:05

score 133 · Answer 4 · 2026-03-26 01:09:40

133

Views

$R$-module isomorphisms $M/A\cong B$ And $M/B\cong A$

Published on 26 Mar 2026 - 1:09

score 374 · Answer 5 · 2022-10-20 02:46:49

374

Views

Are Subgroups' Quotients also Quotients' Subgroups?

Published on 20 Oct 2022 - 2:46

score 73 · Answer 6 · 2022-10-24 07:46:45

73

Views

Quotient group $S_n/A_n$ is abelian?

Published on 24 Oct 2022 - 7:46

score 74 · Answer 7 · 2022-10-29 14:10:54

74

Views

Injection between two groups / homomorphism

Published on 29 Oct 2022 - 14:10

score 48 · Answer 8 · 2022-11-02 14:58:47

48

Views

Compute $T(M)$, where $M=\mathbb{Z}[x]/(x^2-9)$

Published on 02 Nov 2022 - 14:58

score 271 · Answer 9 · 2026-03-28 11:53:29

271

Views

Pocket Cube (2x2x2 Rubik's cube) as Quotient Group

Published on 28 Mar 2026 - 11:53

score 53 · Answer 10 · 2022-11-27 19:22:39

53

Views

Determine the following factor group: $\mathbb{C}^* / \mathbb{R}_{>0}$

Published on 27 Nov 2022 - 19:22

score 66 · Answer 11 · 2022-11-28 02:15:01

66

Views

Let $G=\mathbb{Z}\big /4\mathbb{Z}$ and $H=2\mathbb{Z}\big /4\mathbb{Z}$. Is $H$ isomorphic to $G\big / H$?

Published on 28 Nov 2022 - 2:15

score 43 · Answer 12 · 2026-03-29 18:07:49

43

Views

Show that $D_{2^n}/Z(D_{2^n})\cong D_{2^{n-1}}$.

Published on 29 Mar 2026 - 18:07

score 166 · Answer 13 · 2022-12-14 14:45:13

166

Views

If $M$ and $N$ are normal subgroups of $G$ and $M \subseteq N$, $G/N$ cyclic and $|N/M|=2$ prove that $G/M$ is Abelian.

Published on 14 Dec 2022 - 14:45

score 42 · Answer 14 · 2026-03-22 01:32:35

42

Views

The Basis for the set of cosets (V/U) does not count for (u + U), where u is an element of U (and V)

Published on 22 Mar 2026 - 1:32

score 79 · Answer 15 · 2022-12-18 10:53:33

79

Views

Clarifications on $f:S^n \to S^n$ that is a composition of a quotient map $q: S^n \to \bigvee_k S^n$ and another map $p: \bigvee_k S^n \to S^n$

Published on 18 Dec 2022 - 10:53

List Question

Solvable normal subgroup but the corresponding quotient group is not solvable

Prove or give counter example: $G \cong N \times G/N \Rightarrow N$ has a normal complement.

Nilpotent of subgroup implies nilpotent of group

$R$-module isomorphisms $M/A\cong B$ And $M/B\cong A$

Are Subgroups' Quotients also Quotients' Subgroups?

Quotient group $S_n/A_n$ is abelian?

Injection between two groups / homomorphism

Compute $T(M)$, where $M=\mathbb{Z}[x]/(x^2-9)$

Pocket Cube (2x2x2 Rubik's cube) as Quotient Group

Determine the following factor group: $\mathbb{C}^* / \mathbb{R}_{>0}$

Let $G=\mathbb{Z}\big /4\mathbb{Z}$ and $H=2\mathbb{Z}\big /4\mathbb{Z}$. Is $H$ isomorphic to $G\big / H$?

Show that $D_{2^n}/Z(D_{2^n})\cong D_{2^{n-1}}$.

If $M$ and $N$ are normal subgroups of $G$ and $M \subseteq N$, $G/N$ cyclic and $|N/M|=2$ prove that $G/M$ is Abelian.

The Basis for the set of cosets (V/U) does not count for (u + U), where u is an element of U (and V)

Clarifications on $f:S^n \to S^n$ that is a composition of a quotient map $q: S^n \to \bigvee_k S^n$ and another map $p: \bigvee_k S^n \to S^n$

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