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 123 · Answer 1 · 2018-05-10 01:05:06

123

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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 10 May 2018 - 1:05

score 765 · Answer 2 · 2018-05-12 18:53:32

765

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Can any element of a group generate a cyclic group?

Published on 12 May 2018 - 18:53

score 125 · Answer 3 · 2026-03-24 23:44:55

125

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Cubic cyclic field families

Published on 24 Mar 2026 - 23:44

score 59 · Answer 4 · 2018-05-13 18:50:01

59

Views

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

Published on 13 May 2018 - 18:50

score 1.1k · Answer 5 · 2018-05-15 13:27:00

1.1k

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

Published on 15 May 2018 - 13:27

score 4.1k · Answer 6 · 2018-05-20 17:20:38

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 20 May 2018 - 17:20

score 1.5k · Answer 7 · 2018-05-20 18:47:04

1.5k

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

Published on 20 May 2018 - 18:47

score 68 · Answer 8 · 2018-05-21 19:51:04

68

Views

Prove that $G$ is cyclic

Published on 21 May 2018 - 19:51

score 87 · Answer 9 · 2026-03-25 22:03:59

87

Views

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

Published on 25 Mar 2026 - 22:03

score 412 · Answer 10 · 2018-05-24 08:41:33

412

Views

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

Published on 24 May 2018 - 8:41

score 209 · Answer 11 · 2026-03-25 12:58:28

209

Views

A group with every non-trivial element having infinite order

Published on 25 Mar 2026 - 12:58

score 937 · Answer 12 · 2018-05-25 17:35:42

937

Views

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

Published on 25 May 2018 - 17:35

score 72 · Answer 13 · 2026-03-25 21:40:59

72

Views

Edge-transitive Cayley graphs

Published on 25 Mar 2026 - 21:40

score 294 · Answer 14 · 2026-03-25 13:55:39

294

Views

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

Published on 25 Mar 2026 - 13:55

score 203 · Answer 15 · 2018-05-30 15:19:25

203

Views

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

Published on 30 May 2018 - 15:19

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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