List questions from cyclic-groups

Published on 01 Apr 2026 - 13:43

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Write all permutations in the cyclic group $C_{12}$ of order 12 in cycle notation.

Published on 16 Nov 2021 - 5:07

105

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What does the subgroup generated by a specific 3-cycle look like?

Published on 28 Mar 2026 - 2:03

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Every abelian group of order $9p^2$ where $p\equiv 2\bmod 3$, can be written as the direct product of two cyclic subgroups.

Published on 28 Mar 2026 - 16:25

26

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Count the subgroups of order $25$ in $C_{75} \times C_{10}$

Published on 28 Mar 2026 - 16:26

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How many subgroups does $\mathbb{Z}_{13}\times\mathbb{Z}_{13}$ have?

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61

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Find the order $\bar{5} + H$

Published on 19 Nov 2021 - 15:58

57

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Prove the order of each nonindentity element of $G$ is $p$.

Published on 20 Nov 2021 - 1:49

53

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A Question about a non trivial morphism

Published on 04 Apr 2026 - 11:24

241

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Identity element in a finite cyclic group $G$.

Published on 22 Nov 2021 - 17:30

129

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Let $f: (\Bbb Z_{28}, +)\to(\Bbb Z_{16}, +)$ be a group homomorphism such that $f(1)=12$. Find $\ker f$.

Published on 04 Apr 2026 - 11:28

83

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Homomorphism between cyclic groups is determined by an integer

Published on 04 Apr 2026 - 11:21

35

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If $G$ nilpotent and $G/G'$ is cyclic then $G$ is cyclic?

Published on 23 Feb 2026 - 7:44

105

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If Cylic subgroup implies abelian implies normal then how A5 is simple group

Published on 25 Nov 2021 - 6:32

29

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How to prove if subgroups are Cyclic then Group is Cyclic too?

Published on 28 Nov 2021 - 15:52

List Question

Let $C_n$ be a cyclic group of order $n$. Find all automorphisms of $C_n$.

Write all permutations in the cyclic group $C_{12}$ of order 12 in cycle notation.

What does the subgroup generated by a specific 3-cycle look like?

Every abelian group of order $9p^2$ where $p\equiv 2\bmod 3$, can be written as the direct product of two cyclic subgroups.

Count the subgroups of order $25$ in $C_{75} \times C_{10}$

How many subgroups does $\mathbb{Z}_{13}\times\mathbb{Z}_{13}$ have?

Find the order $\bar{5} + H$

Prove the order of each nonindentity element of $G$ is $p$.

A Question about a non trivial morphism

Identity element in a finite cyclic group $G$.

Let $f: (\Bbb Z_{28}, +)\to(\Bbb Z_{16}, +)$ be a group homomorphism such that $f(1)=12$. Find $\ker f$.

Homomorphism between cyclic groups is determined by an integer

If $G$ nilpotent and $G/G'$ is cyclic then $G$ is cyclic?

If Cylic subgroup implies abelian implies normal then how A5 is simple group

How to prove if subgroups are Cyclic then Group is Cyclic too?

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