Question

Prove $\langle k \rangle / \langle km \rangle \simeq \mathbb {Z}_m,$ where $\langle k \rangle$ is the subgroup generated by $k$ and $k\in \mathbb{Z}$

score 126 · Answer 1 · 2026-04-14 14:34:02

126

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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 14 Apr 2026 - 14:34

score 768 · Answer 2 · 2026-04-10 17:07:15

768

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Can any element of a group generate a cyclic group?

Published on 10 Apr 2026 - 17:07

score 129 · Answer 3 · 2026-05-10 16:10:13

129

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Cubic cyclic field families

Published on 10 May 2026 - 16:10

score 62 · Answer 4 · 2026-04-11 20:58:17

62

Views

How do I prove that $D_3\times \Bbb Z_2$ is not a cyclic group?

Published on 11 Apr 2026 - 20:58

score 1.1k · Answer 5 · 2026-04-15 07:01:11

1.1k

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How to find the number of elements with a particular order in a cyclic group?

Published on 15 Apr 2026 - 7:01

score 4.1k · Answer 6 · 2026-04-14 23:28:48

4.1k

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Suppose that $a$ has order $15$. Find all of the left cosets of $\langle a^5\rangle$ in $\langle a\rangle$ .

Published on 14 Apr 2026 - 23:28

score 1.5k · Answer 7 · 2026-04-11 17:18:00

1.5k

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How to calculate the generators for the multiplicative group $\Bbb Z_4^*$

Published on 11 Apr 2026 - 17:18

score 70 · Answer 8 · 2026-04-14 01:24:26

70

Views

Prove that $G$ is cyclic

Published on 14 Apr 2026 - 1:24

score 90 · Answer 9 · 2026-05-10 17:37:30

90

Views

$H\lhd G$ implies $C_G(h)/C_H(h)$ is cyclic

Published on 10 May 2026 - 17:37

score 415 · Answer 10 · 2026-04-11 13:12:27

415

Views

doubt in proving that an abelian group of order 35 is cyclic.

Published on 11 Apr 2026 - 13:12

score 212 · Answer 11 · 2026-05-10 12:32:35

212

Views

A group with every non-trivial element having infinite order

Published on 10 May 2026 - 12:32

score 940 · Answer 12 · 2026-04-13 21:10:25

940

Views

How to show that any subgroup of a cyclic group must be cyclic

Published on 13 Apr 2026 - 21:10

score 78 · Answer 13 · 2026-04-23 22:20:58

78

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Edge-transitive Cayley graphs

Published on 23 Apr 2026 - 22:20

score 296 · Answer 14 · 2026-04-14 20:24:51

296

Views

$G = \langle a, b : a^3 = b^2 = (ab)^3 = e \rangle$. Find the order of G.

Published on 14 Apr 2026 - 20:24

score 206 · Answer 15 · 2026-04-10 23:09:03

206

Views

Is a finite group union of its cyclic subgroups with trival intersection?

Published on 10 Apr 2026 - 23:09

List Question

Prove $\langle k \rangle / \langle km \rangle \simeq \mathbb {Z}_m,$ where $\langle k \rangle$ is the subgroup generated by $k$ and $k\in \mathbb{Z}$

Can any element of a group generate a cyclic group?

Cubic cyclic field families

How do I prove that $D_3\times \Bbb Z_2$ is not a cyclic group?

How to find the number of elements with a particular order in a cyclic group?

Suppose that $a$ has order $15$. Find all of the left cosets of $\langle a^5\rangle$ in $\langle a\rangle$ .

How to calculate the generators for the multiplicative group $\Bbb Z_4^*$

Prove that $G$ is cyclic

$H\lhd G$ implies $C_G(h)/C_H(h)$ is cyclic

doubt in proving that an abelian group of order 35 is cyclic.

A group with every non-trivial element having infinite order

How to show that any subgroup of a cyclic group must be cyclic

Edge-transitive Cayley graphs

$G = \langle a, b : a^3 = b^2 = (ab)^3 = e \rangle$. Find the order of G.

Is a finite group union of its cyclic subgroups with trival intersection?

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