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Question on a theorem implying a group is cyclic

score 105 · Answer 1 · 2021-07-14 20:12:47

105

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Question on a theorem implying a group is cyclic

Published on 14 Jul 2021 - 20:12

score 167 · Answer 2 · 2026-03-30 15:00:32

167

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Literature on group cohomology of (Z/nZ)* with coefficients in Z/nZ

Published on 30 Mar 2026 - 15:00

score 204 · Answer 3 · 2021-07-25 12:26:20

Suppose $G$ is a cyclic group and $a,b\in G$. There doesn't exist any $x\in G$ such that $x^2=a$ and does not exist any $y\in G$ such that $y^2=b$

score 36 · Answer 4 · 2026-03-28 13:04:35

36

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Proof verification about inexistence of a surjective homomorphism between $C_8\times C_2 \to C_4 \times C_4$

Published on 28 Mar 2026 - 13:04

score 91 · Answer 5 · 2021-08-01 02:40:03

91

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For which prime $p$, is the group units $R^*$ cyclic?

Published on 01 Aug 2021 - 2:40

score 107 · Answer 6 · 2026-03-29 05:12:17

107

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For a group $G$, $N\unlhd G$, $G/N\cong\Bbb{Z}/a\Bbb{Z}$ and $N\cong\Bbb{Z}/b\Bbb{Z}$, where $b<a$ and $(b,a)=1$, show $G$ is abelian.

Published on 29 Mar 2026 - 5:12

score 123 · Answer 7 · 2021-08-08 04:04:13

123

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$\frac{SO(3)\times SO(2)}{SO(2)}$ = $\frac{SO(3)\times\mathbb{R}\times\mathbb{Z}_{2}}{SO(2)\times\mathbb{Z}_{2}}$?

Published on 08 Aug 2021 - 4:04

score 104 · Answer 8 · 2021-08-08 12:23:42

104

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If $G$ is a group, $|G|=8p^n$, $n>1$, $p>7$, $p$-Sylow subgroup is cyclic, prove there is a subgroup with every order $m$ that divides $|G|$

Published on 08 Aug 2021 - 12:23

score 199 · Answer 9 · 2021-08-11 13:27:14

199

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Is $\mathbb{Z}_2 \times \mathbb{Z}_2$ is cyclic ? Yes/No

Published on 11 Aug 2021 - 13:27

score 97 · Answer 10 · 2021-08-13 17:05:51

97

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If $G$ has no proper subgroups then $G$ is cyclical with order $p$, prime.

Published on 13 Aug 2021 - 17:05

score 48 · Answer 11 · 2021-08-14 12:21:22

48

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Let $G$ be finite s.t. there exists an epimorphism $\varphi: G\to\Bbb{Z}_2\times\Bbb{Z}_2\times\Bbb{Z}_3$. Show $G$ has no cyclic Sylow $2$-subgroup.

Published on 14 Aug 2021 - 12:21

score 179 · Answer 12 · 2021-08-14 15:03:33

179

Views

Is $\mathbb{Z}_2 \times \mathbb{Z}$ is cyclic? True/false

Published on 14 Aug 2021 - 15:03

score 135 · Answer 13 · 2026-02-23 07:23:07

135

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The characteristic subgroup of order $m$ (odd) in a group of order $2^nm$ with cyclic 2-sylow

Published on 23 Feb 2026 - 7:23

score 78 · Answer 14 · 2021-08-22 06:01:34

78

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How many number of cyclic subgroup of order $12$ of $\mathbb Z/2\mathbb Z×\mathbb Z/3\mathbb Z×\mathbb Z/3\mathbb Z ×\mathbb Z/4\mathbb Z$?

Published on 22 Aug 2021 - 6:01

score 116 · Answer 15 · 2026-03-29 03:36:18

116

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We have $N\unlhd G$, a cyclic subgroup of order $n$, $G/N$ cyclic group of order $m$ s.t. $\gcd(m,\phi(n))=1$. Show $G$ is abelian.

Published on 29 Mar 2026 - 3:36

List Question

Question on a theorem implying a group is cyclic

Literature on group cohomology of (Z/nZ)* with coefficients in Z/nZ

Suppose $G$ is a cyclic group and $a,b\in G$. There doesn't exist any $x\in G$ such that $x^2=a$ and does not exist any $y\in G$ such that $y^2=b$

Proof verification about inexistence of a surjective homomorphism between $C_8\times C_2 \to C_4 \times C_4$

For which prime $p$, is the group units $R^*$ cyclic?

For a group $G$, $N\unlhd G$, $G/N\cong\Bbb{Z}/a\Bbb{Z}$ and $N\cong\Bbb{Z}/b\Bbb{Z}$, where $b<a$ and $(b,a)=1$, show $G$ is abelian.

$\frac{SO(3)\times SO(2)}{SO(2)}$ = $\frac{SO(3)\times\mathbb{R}\times\mathbb{Z}_{2}}{SO(2)\times\mathbb{Z}_{2}}$?

If $G$ is a group, $|G|=8p^n$, $n>1$, $p>7$, $p$-Sylow subgroup is cyclic, prove there is a subgroup with every order $m$ that divides $|G|$

Is $\mathbb{Z}_2 \times \mathbb{Z}_2$ is cyclic ? Yes/No

If $G$ has no proper subgroups then $G$ is cyclical with order $p$, prime.

Let $G$ be finite s.t. there exists an epimorphism $\varphi: G\to\Bbb{Z}_2\times\Bbb{Z}_2\times\Bbb{Z}_3$. Show $G$ has no cyclic Sylow $2$-subgroup.

Is $\mathbb{Z}_2 \times \mathbb{Z}$ is cyclic? True/false

The characteristic subgroup of order $m$ (odd) in a group of order $2^nm$ with cyclic 2-sylow

How many number of cyclic subgroup of order $12$ of $\mathbb Z/2\mathbb Z×\mathbb Z/3\mathbb Z×\mathbb Z/3\mathbb Z ×\mathbb Z/4\mathbb Z$?

We have $N\unlhd G$, a cyclic subgroup of order $n$, $G/N$ cyclic group of order $m$ s.t. $\gcd(m,\phi(n))=1$. Show $G$ is abelian.

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