Question

Number of roots of unity in a finite cyclic group G, source to cite

score 68 · Answer 1 · 2026-04-02 19:02:40

68

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Number of roots of unity in a finite cyclic group G, source to cite

Published on 02 Apr 2026 - 19:02

score 178 · Answer 2 · 2021-06-07 10:57:04

178

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Order of elements in the multiplicative group of the finite field extension

Published on 07 Jun 2021 - 10:57

score 228 · Answer 3 · 2026-03-29 06:28:43

228

Views

Prove that $D_{12}$ is not cyclic.

Published on 29 Mar 2026 - 6:28

score 511 · Answer 4 · 2021-06-14 06:54:55

511

Views

How to show that group of order 15 is cyclic?

Published on 14 Jun 2021 - 6:54

score 65 · Answer 5 · 2021-06-15 21:13:30

65

Views

Computing $\operatorname{Hom}_{\mathbb{Z}}(G, C_p)$

Published on 15 Jun 2021 - 21:13

score 108 · Answer 6 · 2021-06-16 15:32:19

108

Views

number of subgroups $H$ of $\mathbb{Z}_{p^2} \times \mathbb{Z}_{p^3}$ with $|H|=p^2$.

Published on 16 Jun 2021 - 15:32

score 124 · Answer 7 · 2026-03-25 15:42:22

124

Views

Let $G$ be a $p$-group. If every two maximal subgroups of $G$ are conjugated, then $G$ is cyclic

Published on 25 Mar 2026 - 15:42

score 855 · Answer 8 · 2021-06-28 12:56:44

855

Views

Let $G$ be a finite cyclic group. Prove that if $n$ is a divisor of $|G|$ then there exists an element of order $n$ in $G$.

Published on 28 Jun 2021 - 12:56

score 61 · Answer 9 · 2021-06-28 13:10:36

61

Views

Let $P$ be a Sylow $p$-subgroup of $G$ and suppose $x\in P$ has order $p$ and $C_G(x)$ has cyclic Sylow $p$-subgroups. Prove $P$ is cyclic.

Published on 28 Jun 2021 - 13:10

score 121 · Answer 10 · 2021-07-03 05:56:57

121

Views

How to show that two subgroups of $\mathbb Z_n$ are equal

Published on 03 Jul 2021 - 5:56

score 256 · Answer 11 · 2026-03-28 21:26:49

256

Views

Why is $S_3 / A_3$ cyclic group of order $2$?

Published on 28 Mar 2026 - 21:26

score 64 · Answer 12 · 2021-07-06 22:12:10

64

Views

Clarification on proof that subgroup of cyclic group is cyclic

Published on 06 Jul 2021 - 22:12

score 214 · Answer 13 · 2021-07-09 15:15:55

214

Views

Are all bijections from a finite cyclic group to itself isomorphisms, if generators are mapped only to generators?

Published on 09 Jul 2021 - 15:15

score 1.1k · Answer 14 · 2021-07-11 04:23:59

1.1k

Views

A non-cyclic finite abelian group contains a subgroup isomorphic to the direct product of a group of order $p$ with itself

Published on 11 Jul 2021 - 4:23

score 132 · Answer 15 · 2021-07-13 14:20:52

132

Views

Find all the cyclic subgroups of $\mathbb{Z}_{p^r} \times \mathbb{Z}_{p^r}$ of order $p^r$

Published on 13 Jul 2021 - 14:20

List Question

Number of roots of unity in a finite cyclic group G, source to cite

Order of elements in the multiplicative group of the finite field extension

Prove that $D_{12}$ is not cyclic.

How to show that group of order 15 is cyclic?

Computing $\operatorname{Hom}_{\mathbb{Z}}(G, C_p)$

number of subgroups $H$ of $\mathbb{Z}_{p^2} \times \mathbb{Z}_{p^3}$ with $|H|=p^2$.

Let $G$ be a $p$-group. If every two maximal subgroups of $G$ are conjugated, then $G$ is cyclic

Let $G$ be a finite cyclic group. Prove that if $n$ is a divisor of $|G|$ then there exists an element of order $n$ in $G$.

Let $P$ be a Sylow $p$-subgroup of $G$ and suppose $x\in P$ has order $p$ and $C_G(x)$ has cyclic Sylow $p$-subgroups. Prove $P$ is cyclic.

How to show that two subgroups of $\mathbb Z_n$ are equal

Why is $S_3 / A_3$ cyclic group of order $2$?

Clarification on proof that subgroup of cyclic group is cyclic

Are all bijections from a finite cyclic group to itself isomorphisms, if generators are mapped only to generators?

A non-cyclic finite abelian group contains a subgroup isomorphic to the direct product of a group of order $p$ with itself

Find all the cyclic subgroups of $\mathbb{Z}_{p^r} \times \mathbb{Z}_{p^r}$ of order $p^r$

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