List questions from cyclic-groups

Published on 29 Jan 2017 - 19:04

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Finding generators of the group $m\mathbb{Z}+n\mathbb{Z}$

Published on 30 Jan 2017 - 19:59

76

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Cyclic sub groups groups proof

Published on 31 Jan 2017 - 16:32

126

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The automorphisms of the Cayley diagram of the cyclic group

Published on 26 Mar 2026 - 4:36

73

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Generated Subgroup of $\mathbb{Z}$?

Published on 02 Feb 2017 - 21:29

1.6k

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Structure of $Z/nZ$

Published on 05 Feb 2017 - 19:56

1k

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$(G:H) < \infty$ where $G$ is an infinite cyclic group

Published on 12 Feb 2017 - 11:08

598

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Show that $\operatorname{Aut}(C_{14})$ is a cyclic group.

Published on 12 Feb 2017 - 17:30

89

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Understanding Cayleys Theorem

Published on 25 Mar 2026 - 1:31

4.1k

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Group $(\mathbb{Z}^*_{13}, \cdot)$, calculate order of the group, if it's a cyclic group, and the order of all its elements

Published on 13 Feb 2017 - 20:27

16

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given two disjoint β and α, prove that ραρ−1 and ρβρ−1 are disjoint

Published on 10 Mar 2026 - 10:06

325

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If $G = C_{25}\times C_{45}\times C_{48}\times C_{150}$, How many subgroups of order $5$ does $G$ have?

Published on 14 Feb 2017 - 14:37

2k

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Obtain the elements of a subgroup generated from a permutation, given the elements of the subgroups generated from its disjoint cycles.

Published on 15 Feb 2017 - 21:14

127

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Given a free group of rank $n$, a non-identity $g$, normalizer of $\langle g\rangle$ is cyclic

Published on 26 Mar 2026 - 22:18

80

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$p \equiv 1 \mod 3$, prove: there is an $x \in \mathbb{Z}$ such that $ x^2 \equiv -3 \mod p$.

Published on 20 Feb 2017 - 16:57

List Question

How do I see a group's generator?

Finding generators of the group $m\mathbb{Z}+n\mathbb{Z}$

Cyclic sub groups groups proof

The automorphisms of the Cayley diagram of the cyclic group

Generated Subgroup of $\mathbb{Z}$?

Structure of $Z/nZ$

$(G:H) < \infty$ where $G$ is an infinite cyclic group

Show that $\operatorname{Aut}(C_{14})$ is a cyclic group.

Understanding Cayleys Theorem

Group $(\mathbb{Z}^*_{13}, \cdot)$, calculate order of the group, if it's a cyclic group, and the order of all its elements

given two disjoint β and α, prove that ραρ−1 and ρβρ−1 are disjoint

If $G = C_{25}\times C_{45}\times C_{48}\times C_{150}$, How many subgroups of order $5$ does $G$ have?

Obtain the elements of a subgroup generated from a permutation, given the elements of the subgroups generated from its disjoint cycles.

Given a free group of rank $n$, a non-identity $g$, normalizer of $\langle g\rangle$ is cyclic

$p \equiv 1 \mod 3$, prove: there is an $x \in \mathbb{Z}$ such that $ x^2 \equiv -3 \mod p$.

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