List questions from cyclic-groups

Published on 29 Mar 2026 - 20:04

74

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Preimage of an Abelian/Cyclic tower is an Abelian/Cyclic tower

Published on 30 Mar 2026 - 0:21

79

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Identify the group $(28\mathbb Z + 20\mathbb Z)/20 \mathbb Z$

Published on 26 Mar 2026 - 21:07

145

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Relationship between periodic groups and cyclic groups

Published on 10 Feb 2023 - 7:42

701

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Concrete example of a cyclic group?

Published on 11 Feb 2023 - 20:42

222

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On the cyclicity of $\operatorname{Aut}(\Bbb Z/p\Bbb Z)$, for $p$ a prime.

Published on 29 Mar 2026 - 20:11

63

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$\Sigma\le S_n$ of order $n$. Is $\Sigma$ cyclic, if each $\tau\in\Sigma\setminus\{Id\}$ moves all the elements?

Published on 30 Mar 2026 - 22:49

200

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How do you verify that $(1,2)$ is a generator of $\mathbb{Z}_2 \times \mathbb{Z}_5$? (Abstract Algebra Question)

Published on 15 Feb 2023 - 3:08

94

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I dont understand why every sub group of cyclic groups are also cyclic.

Published on 15 Feb 2023 - 19:11

303

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Prove or disprove : All of the generators greater than $1$ of $\Bbb Z_{60}$ are prime.

Published on 15 Feb 2023 - 23:37

287

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Cyclic Group Order of Elements

Published on 19 Feb 2023 - 4:18

109

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If an abelian group contains at most $n$ elements of order divisible by $n$, is it cyclic?

Published on 19 Feb 2023 - 6:40

556

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Help on proof that if (G,$\cdot$) is a cyclic group generated by $g^n$, then G is also generated by $g$.

Published on 20 Feb 2023 - 18:08

66

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The stabilizer of a cyclic group over a group algebra

Published on 23 Feb 2026 - 10:03

95

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What is the order of a group given three generators, $a^2=b^3=c^4=1$ and $cb=ac$

Published on 26 Mar 2026 - 19:03

List Question

Showing ${\rm Aut}(\Bbb Z_{70})$ is abelian

Preimage of an Abelian/Cyclic tower is an Abelian/Cyclic tower

Identify the group $(28\mathbb Z + 20\mathbb Z)/20 \mathbb Z$

Relationship between periodic groups and cyclic groups

Concrete example of a cyclic group?

On the cyclicity of $\operatorname{Aut}(\Bbb Z/p\Bbb Z)$, for $p$ a prime.

$\Sigma\le S_n$ of order $n$. Is $\Sigma$ cyclic, if each $\tau\in\Sigma\setminus\{Id\}$ moves all the elements?

How do you verify that $(1,2)$ is a generator of $\mathbb{Z}_2 \times \mathbb{Z}_5$? (Abstract Algebra Question)

I dont understand why every sub group of cyclic groups are also cyclic.

Prove or disprove : All of the generators greater than $1$ of $\Bbb Z_{60}$ are prime.

Cyclic Group Order of Elements

If an abelian group contains at most $n$ elements of order divisible by $n$, is it cyclic?

Help on proof that if (G,$\cdot$) is a cyclic group generated by $g^n$, then G is also generated by $g$.

The stabilizer of a cyclic group over a group algebra

What is the order of a group given three generators, $a^2=b^3=c^4=1$ and $cb=ac$

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