Question

Can $G/H$ be cyclic if $G$ is nonabelian?

score 576 · Answer 1 · 2026-03-26 04:31:14

576

Views

Can $G/H$ be cyclic if $G$ is nonabelian?

Published on 26 Mar 2026 - 4:31

score 920 · Answer 2 · 2026-03-29 04:53:35

920

Views

Automorphism Group isomorphic to $\mathbb{Z}_n$

Published on 29 Mar 2026 - 4:53

score 93 · Answer 3 · 2026-03-28 11:35:28

93

Views

Determine the least positive integer $n$ for which the cyclic group $(\Bbb Z_{60},+\pmod{60})$ is isomorphic to a subgroup of $S_n$.

Published on 28 Mar 2026 - 11:35

score 31 · Answer 4 · 2019-11-21 14:40:32

31

Views

Metacyclic group acting on a vector space

Published on 21 Nov 2019 - 14:40

score 65 · Answer 5 · 2026-03-29 11:50:13

65

Views

How do you show that the cyclic group $C_4$ is a subgroup of the Quaternion group?

Published on 29 Mar 2026 - 11:50

score 173 · Answer 6 · 2019-11-22 00:52:37

173

Views

Let $G$ be a group, $k$ be a positive integer, $G^k=\{ g^k \mid g\in G\}$. Prove that $G$ is cyclic iff every subgroup of $G$ has a set form $G^k$.

Published on 22 Nov 2019 - 0:52

score 311 · Answer 7 · 2019-11-23 15:55:52

311

Views

Prove that center of $G$ is not trivial and $G$ is a cyclic group

Published on 23 Nov 2019 - 15:55

score 194 · Answer 8 · 2019-11-24 23:08:12

194

Views

Jordan-Hölder composition series of the additive group $\mathbb{Z}/a\mathbb{Z}$ of integers modulo a

Published on 24 Nov 2019 - 23:08

score 61 · Answer 9 · 2026-03-25 19:01:24

61

Views

difference between Cyclic subspace and f-Invariant subspace

Published on 25 Mar 2026 - 19:01

score 672 · Answer 10 · 2026-03-25 19:04:57

672

Views

What is the meaning of $\langle x\rangle$ in group theory?

Published on 25 Mar 2026 - 19:04

score 192 · Answer 11 · 2019-11-29 15:22:39

192

Views

Show that the multiplicative group $K^{\times}=K \setminus \{0\}$ is not cyclic.

Published on 29 Nov 2019 - 15:22

score 54 · Answer 12 · 2019-11-29 16:55:41

54

Views

Prove that $K^{\times}=\langle \alpha \rangle$ where $\alpha$ is transcendental cannot be true.

Published on 29 Nov 2019 - 16:55

score 193 · Answer 13 · 2026-03-26 12:49:21

193

Views

Generators of a direct product of $\Bbb Z_2$ with $\Bbb Z_4$.

Published on 26 Mar 2026 - 12:49

score 161 · Answer 14 · 2026-03-26 07:44:12

161

Views

$G\:/\:H$, where $G = \mathbb{Z} \oplus \mathbb{Z}$ and $H = \langle(1,3) , (3,1)\rangle$

Published on 26 Mar 2026 - 7:44

score 63 · Answer 15 · 2026-03-25 03:03:02

63

Views

Describing the product of two Artin characters

Published on 25 Mar 2026 - 3:03

List Question

Can $G/H$ be cyclic if $G$ is nonabelian?

Automorphism Group isomorphic to $\mathbb{Z}_n$

Determine the least positive integer $n$ for which the cyclic group $(\Bbb Z_{60},+\pmod{60})$ is isomorphic to a subgroup of $S_n$.

Metacyclic group acting on a vector space

How do you show that the cyclic group $C_4$ is a subgroup of the Quaternion group?

Let $G$ be a group, $k$ be a positive integer, $G^k=\{ g^k \mid g\in G\}$. Prove that $G$ is cyclic iff every subgroup of $G$ has a set form $G^k$.

Prove that center of $G$ is not trivial and $G$ is a cyclic group

Jordan-Hölder composition series of the additive group $\mathbb{Z}/a\mathbb{Z}$ of integers modulo a

difference between Cyclic subspace and f-Invariant subspace

What is the meaning of $\langle x\rangle$ in group theory?

Show that the multiplicative group $K^{\times}=K \setminus \{0\}$ is not cyclic.

Prove that $K^{\times}=\langle \alpha \rangle$ where $\alpha$ is transcendental cannot be true.

Generators of a direct product of $\Bbb Z_2$ with $\Bbb Z_4$.

$G\:/\:H$, where $G = \mathbb{Z} \oplus \mathbb{Z}$ and $H = \langle(1,3) , (3,1)\rangle$

Describing the product of two Artin characters

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