List questions from cyclic-groups

Published on 03 Apr 2016 - 14:48

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Proof groups equality: $\langle x^{t_1},x^{t_2} \rangle = \langle x^{\gcd(t_1,t_2,n)} \rangle$

Published on 06 Apr 2016 - 10:03

67

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Number of elements in factorgroup

Published on 10 Apr 2016 - 12:38

28

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Suppose that $H$ is a (cyclic) subgroup of order $m$ of a cyclic (abelian) group $G$ of order $n$. What is $G/H$?

Published on 10 Apr 2016 - 20:22

104

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$\mathbb Z_n^*$ has a unique subgroup of order $2$ then it is cyclic for $n >2$

Published on 12 Apr 2016 - 16:00

578

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Proving that a Galois group is cyclic

Published on 29 Mar 2026 - 17:31

422

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Subgroups of the Semi-Direct Product $\mathbb{Z}/7\mathbb{Z} \rtimes (\mathbb{Z}/7\mathbb{Z})^{\times}$

Published on 29 Mar 2026 - 18:32

31

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Consider a set consisting of matrices and show it is a group.

Published on 14 Apr 2016 - 16:39

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Proof for generator of the group of integer under addition modulo

Published on 16 Apr 2016 - 4:02

107

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showing the inverse of an element is a generator of the non-inverse

Published on 17 Apr 2016 - 1:26

2k

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Element of infinite order and all generator of subgroups

Published on 17 Apr 2016 - 3:30

164

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Show that $|a^{k}|=|a^{n-k}|$

Published on 18 Apr 2016 - 4:05

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If $G/Z(G)$ is cyclic, why is $G$ only abelian and not also cyclic?

Published on 19 Apr 2016 - 18:21

101

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Proving existence of automorphism

Published on 21 Apr 2016 - 13:55

80

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Conway's theorem on the number of orbits on the set of all ordered cycles in a $d$-valent graph

Published on 27 Mar 2026 - 13:20

List Question

$\sum_{d|n} \varphi(d)=n$

Proof groups equality: $\langle x^{t_1},x^{t_2} \rangle = \langle x^{\gcd(t_1,t_2,n)} \rangle$

Number of elements in factorgroup

Suppose that $H$ is a (cyclic) subgroup of order $m$ of a cyclic (abelian) group $G$ of order $n$. What is $G/H$?

$\mathbb Z_n^*$ has a unique subgroup of order $2$ then it is cyclic for $n >2$

Proving that a Galois group is cyclic

Subgroups of the Semi-Direct Product $\mathbb{Z}/7\mathbb{Z} \rtimes (\mathbb{Z}/7\mathbb{Z})^{\times}$

Consider a set consisting of matrices and show it is a group.

Proof for generator of the group of integer under addition modulo

showing the inverse of an element is a generator of the non-inverse

Element of infinite order and all generator of subgroups

Show that $|a^{k}|=|a^{n-k}|$

If $G/Z(G)$ is cyclic, why is $G$ only abelian and not also cyclic?

Proving existence of automorphism

Conway's theorem on the number of orbits on the set of all ordered cycles in a $d$-valent graph

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