List questions from cyclic-groups

Published on 18 Sep 2020 - 14:10

277

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Show that if $G$ is a cyclic group of order $p^n-1$ ($p-$ prime) then every element of G can be written in the form $a^p$, $a \in G$

Published on 18 Sep 2020 - 14:26

504

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To find the number of Elements of order 4 in Galois Field $GF(p^n)^*$,

Published on 29 Mar 2026 - 22:33

187

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Is $\mathcal{O}_K^{\times}$ a cyclic group just like $\mathbb{Z}^{\times}$?

Published on 22 Sep 2020 - 13:14

42

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Multiplicative Groups and Non-Natural numbers

Published on 22 Sep 2020 - 14:34

697

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Subgroups of order $p^2$ of $Z_{p^2} \times Z_p$

Published on 30 Sep 2020 - 17:19

52

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Are infinite cyclic normal subgroups "virtually" central?

Published on 27 Mar 2026 - 19:30

299

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Is the quotient group $\mathbb{Z}_4 \times \mathbb{Z}_6 / \langle(2,2)\rangle$ cyclic?

Published on 28 Mar 2026 - 1:48

197

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Dummit and Foote 2.4.14c

Published on 02 Oct 2020 - 4:18

32

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Need help understanding example of semidirect product (continued)

Published on 30 Mar 2026 - 8:05

297

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Dumbing down Proposition 3.1, Lang's Algebra p. 18 (abelian towers, cyclic refinements)

Published on 27 Mar 2026 - 21:59

4.5k

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How can Cyclic groups be infinite

Published on 27 Mar 2026 - 19:29

250

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Checking whether the group generated by a set is normal

Published on 29 Mar 2026 - 18:36

72

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Check if an element is in a cyclic group

Published on 06 Oct 2020 - 19:04

718

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Find smallest subgroups

Published on 27 Mar 2026 - 19:30

List Question

Show that $U(17)$ is a cyclic group

Show that if $G$ is a cyclic group of order $p^n-1$ ($p-$ prime) then every element of G can be written in the form $a^p$, $a \in G$

To find the number of Elements of order 4 in Galois Field $GF(p^n)^*$,

Is $\mathcal{O}_K^{\times}$ a cyclic group just like $\mathbb{Z}^{\times}$?

Multiplicative Groups and Non-Natural numbers

Subgroups of order $p^2$ of $Z_{p^2} \times Z_p$

Are infinite cyclic normal subgroups "virtually" central?

Is the quotient group $\mathbb{Z}_4 \times \mathbb{Z}_6 / \langle(2,2)\rangle$ cyclic?

Dummit and Foote 2.4.14c

Need help understanding example of semidirect product (continued)

Dumbing down Proposition 3.1, Lang's Algebra p. 18 (abelian towers, cyclic refinements)

How can Cyclic groups be infinite

Checking whether the group generated by a set is normal

Check if an element is in a cyclic group

Find smallest subgroups

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