Question

Let $G$ be a cyclic group of order $n$. Then what can we say about n?

score 73 · Answer 1 · 2017-05-22 17:28:26

73

Views

Let $G$ be a cyclic group of order $n$. Then what can we say about n?

Published on 22 May 2017 - 17:28

score 109 · Answer 2 · 2017-05-23 03:49:16

109

Views

Prove that if $p$ is a prime and $p\ne 2$, then $(\Bbb Z/p^n \Bbb Z)^*$ is cyclic

Published on 23 May 2017 - 3:49

score 862 · Answer 3 · 2017-05-23 10:02:41

862

Views

Condition(s) for a generator to be mapped to a generator by a homomorphism?

Published on 23 May 2017 - 10:02

score 765 · Answer 4 · 2017-05-25 16:35:01

765

Views

Generator polynomial cyclic codes

Published on 25 May 2017 - 16:35

score 110 · Answer 5 · 2026-04-03 06:36:04

110

Views

Which of the following groups are isomorphic? Choose from 4.

Published on 03 Apr 2026 - 6:36

score 2.8k · Answer 6 · 2017-05-27 04:15:09

2.8k

Views

Which of the following group has a proper subgroup that is not cyclic?

Published on 27 May 2017 - 4:15

score 5.2k · Answer 7 · 2017-05-27 13:44:58

5.2k

Views

Proving that a group of order $77$ is cyclic.

Published on 27 May 2017 - 13:44

score 39 · Answer 8 · 2017-05-31 19:43:33

39

Views

Let $H$ be the semidirect product of $A$ and $B$ with respect to $\phi$. List all the elements in the centre $Z(H)$ of $H$.

Published on 31 May 2017 - 19:43

score 149 · Answer 9 · 2017-06-01 09:18:32

149

Views

Show that G is a cyclic group and show that there are proper subgroups $H$ and $K$ of $H$ such that $G\cong G/H \times G/K$

Published on 01 Jun 2017 - 9:18

score 47 · Answer 10 · 2017-06-01 15:00:53

47

Views

Find the order of $G=C_3 \times \mathbb{Z}_5 \times S_4$.

Published on 01 Jun 2017 - 15:00

score 138 · Answer 11 · 2017-06-01 17:22:22

138

Views

why does an infinite cyclic group need to be infinite on both sides?

Published on 01 Jun 2017 - 17:22

score 65 · Answer 12 · 2017-06-04 14:11:51

65

Views

Proof that $ (\mathbb{Z} \times \mathbb{Z},+) /\langle(2,3)\rangle $ is cyclic.

Published on 04 Jun 2017 - 14:11

score 517 · Answer 13 · 2017-06-05 01:35:34

517

Views

Determining if a factor group is cyclic.

Published on 05 Jun 2017 - 1:35

score 494 · Answer 14 · 2026-03-28 08:09:30

494

Views

If $ |G|=2 p$ then either $G$ is cyclic or $G \cong D_{2\cdot p}$

Published on 28 Mar 2026 - 8:09

score 292 · Answer 15 · 2017-06-08 21:04:47

292

Views

Proposition $5.2$, Section $2.3$ (Cyclic Groups) in Dummit and Foote's Abstract Algebra

Published on 08 Jun 2017 - 21:04

List Question

Let $G$ be a cyclic group of order $n$. Then what can we say about n?

Prove that if $p$ is a prime and $p\ne 2$, then $(\Bbb Z/p^n \Bbb Z)^*$ is cyclic

Condition(s) for a generator to be mapped to a generator by a homomorphism?

Generator polynomial cyclic codes

Which of the following groups are isomorphic? Choose from 4.

Which of the following group has a proper subgroup that is not cyclic?

Proving that a group of order $77$ is cyclic.

Let $H$ be the semidirect product of $A$ and $B$ with respect to $\phi$. List all the elements in the centre $Z(H)$ of $H$.

Show that G is a cyclic group and show that there are proper subgroups $H$ and $K$ of $H$ such that $G\cong G/H \times G/K$

Find the order of $G=C_3 \times \mathbb{Z}_5 \times S_4$.

why does an infinite cyclic group need to be infinite on both sides?

Proof that $ (\mathbb{Z} \times \mathbb{Z},+) /\langle(2,3)\rangle $ is cyclic.

Determining if a factor group is cyclic.

If $ |G|=2 p$ then either $G$ is cyclic or $G \cong D_{2\cdot p}$

Proposition $5.2$, Section $2.3$ (Cyclic Groups) in Dummit and Foote's Abstract Algebra

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