List questions from cyclic-groups

Published on 27 Mar 2026 - 13:47

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Prove that the subgroup of the quotient group is cycling and infinitely generated

Published on 04 Jan 2014 - 22:35

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quotient group Z/3Z equated to 0,1,2

Published on 05 Jan 2014 - 9:29

1.3k

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Number of elements which are cubes/higher powers in a finite field.

Published on 05 Jan 2014 - 14:05

313

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subgroups of finite cyclic group

Published on 07 Jan 2014 - 17:38

145

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If $\chi(a)=1$ for all $\chi\in\hat G$ then $a=0$.

Published on 28 Mar 2026 - 20:11

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Cyclic Group Problem

Published on 10 Jan 2014 - 16:06

71

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Simple question regarding number of elements in cyclic subgroups

Published on 10 Jan 2014 - 21:13

259

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Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$

Published on 15 Jan 2014 - 3:52

191

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A question about permutation and cyclic group

Published on 15 Jan 2014 - 17:15

117

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If $\sigma\in S_n$ is of length $n$, then $\sigma$ generates its centralizer

Published on 15 Jan 2014 - 21:13

84

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Divisors of the totient function and congruences

Published on 16 Jan 2014 - 8:52

107

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Fast way of calculating the order of an element in $\mathbb{Z}_n$?

Published on 16 Jan 2014 - 17:25

17.6k

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Find all proper nontrivial subgroups of $\mathbb Z_2 \times \mathbb Z_2 \times \mathbb Z_2$ - Fraleigh p. 110 Exercise 11.10

Published on 19 Jan 2014 - 8:24

1.3k

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Find all subgroups of $\mathbb Z_2\times\mathbb Z_4$ - Fraleigh p. 110 Exercise 1.11

Published on 19 Jan 2014 - 9:33

List Question

Counting Elements of Order $2$ in a Direct Product of Cyclic Groups

Prove that the subgroup of the quotient group is cycling and infinitely generated

quotient group Z/3Z equated to 0,1,2

Number of elements which are cubes/higher powers in a finite field.

subgroups of finite cyclic group

If $\chi(a)=1$ for all $\chi\in\hat G$ then $a=0$.

Cyclic Group Problem

Simple question regarding number of elements in cyclic subgroups

Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$

A question about permutation and cyclic group

If $\sigma\in S_n$ is of length $n$, then $\sigma$ generates its centralizer

Divisors of the totient function and congruences

Fast way of calculating the order of an element in $\mathbb{Z}_n$?

Find all proper nontrivial subgroups of $\mathbb Z_2 \times \mathbb Z_2 \times \mathbb Z_2$ - Fraleigh p. 110 Exercise 11.10

Find all subgroups of $\mathbb Z_2\times\mathbb Z_4$ - Fraleigh p. 110 Exercise 1.11

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