Question

Prove that any group of order 15 is cyclic?

score 603 · Answer 1 · 2021-11-28 18:07:50

603

Views

Prove that any group of order 15 is cyclic?

Published on 28 Nov 2021 - 18:07

score 113 · Answer 2 · 2026-03-28 16:26:26

113

Views

Quotient of the direct product of cyclic groups

Published on 28 Mar 2026 - 16:26

score 119 · Answer 3 · 2021-12-02 09:46:26

119

Views

After using Sylow Theorems, how can we say how many elements of order 5 might be there in a group of order 20?

Published on 02 Dec 2021 - 9:46

score 1.2k · Answer 4 · 2021-12-03 22:12:58

1.2k

Views

Let $G$ be a finite Abelian group that has exactly one subgroup for each divisor of $|G|$. How does this imply that $G$ is cyclic?

Published on 03 Dec 2021 - 22:12

score 65 · Answer 5 · 2021-12-05 15:23:17

65

Views

Show by giving a counterexample that $H \cap N$ is not necessarily a normal subgroup of $G$.

Published on 05 Dec 2021 - 15:23

score 250 · Answer 6 · 2026-04-01 15:08:30

250

Views

A proof attempt of the cyclicity of $(\Bbb Z/p\Bbb Z)^\times$

Published on 01 Apr 2026 - 15:08

score 80 · Answer 7 · 2021-12-07 19:32:41

80

Views

if $x$ and $y$ are commuting and have coprime orders then $\langle x,y\rangle $ is cyclic

Published on 07 Dec 2021 - 19:32

score 36 · Answer 8 · 2021-12-09 11:47:00

36

Views

Let $n$ be a positive integer and $k \in \Bbb Z$. Show that $\langle [k]_n \rangle$ is an ideal for $(\Bbb Z_n, +, \cdot)$.

Published on 09 Dec 2021 - 11:47

score 130 · Answer 9 · 2021-12-09 17:28:04

130

Views

if $G$ only has one subgroup of order $p$ and one subgroup of order $q$, then $G$ is a cyclic group

Published on 09 Dec 2021 - 17:28

score 641 · Answer 10 · 2021-12-10 08:24:08

641

Views

Given $G=\langle a\rangle$, $|G|=n$ and $d\mid n$, show $G$ has a unique subgroup of order $d$.

Published on 10 Dec 2021 - 8:24

score 99 · Answer 11 · 2021-12-10 11:00:27

99

Views

Is $(\mathbb{Q^+},\cdot)$ cyclic?

Published on 10 Dec 2021 - 11:00

score 82 · Answer 12 · 2026-03-30 07:39:09

82

Views

Help with proof on finitely generated abelian groups and its product of cyclic groups

Published on 30 Mar 2026 - 7:39

score 162 · Answer 13 · 2021-12-11 21:18:28

162

Views

How to prove that $\mathbb{C}_n$ is a subgroup of $(\Bbb C\setminus\{0\},\cdot)$.

Published on 11 Dec 2021 - 21:18

score 67 · Answer 14 · 2026-03-29 05:34:55

67

Views

Cyclicness of a quotient of subgroups of infinite cyclic group

Published on 29 Mar 2026 - 5:34

score 21 · Answer 15 · 2026-03-29 11:43:37

21

Views

Working out cyclic subgroups of $D_{8}$

Published on 29 Mar 2026 - 11:43

List Question

Prove that any group of order 15 is cyclic?

Quotient of the direct product of cyclic groups

After using Sylow Theorems, how can we say how many elements of order 5 might be there in a group of order 20?

Let $G$ be a finite Abelian group that has exactly one subgroup for each divisor of $|G|$. How does this imply that $G$ is cyclic?

Show by giving a counterexample that $H \cap N$ is not necessarily a normal subgroup of $G$.

A proof attempt of the cyclicity of $(\Bbb Z/p\Bbb Z)^\times$

if $x$ and $y$ are commuting and have coprime orders then $\langle x,y\rangle $ is cyclic

Let $n$ be a positive integer and $k \in \Bbb Z$. Show that $\langle [k]_n \rangle$ is an ideal for $(\Bbb Z_n, +, \cdot)$.

if $G$ only has one subgroup of order $p$ and one subgroup of order $q$, then $G$ is a cyclic group

Given $G=\langle a\rangle$, $|G|=n$ and $d\mid n$, show $G$ has a unique subgroup of order $d$.

Is $(\mathbb{Q^+},\cdot)$ cyclic?

Help with proof on finitely generated abelian groups and its product of cyclic groups

How to prove that $\mathbb{C}_n$ is a subgroup of $(\Bbb C\setminus\{0\},\cdot)$.

Cyclicness of a quotient of subgroups of infinite cyclic group

Working out cyclic subgroups of $D_{8}$

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