List questions from cyclic-groups

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Proof check: Necessary and sufficient condition for $\langle x^r\rangle\subseteq\langle x^s\rangle$?

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Confused about cyclic goups

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Does my claim work for a set?

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Let $G$ be a finite nilpotent group and $G'$ its commutator subgroup. Show that if $G/G'$ is cyclic then $G$ is cyclic.

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A question on infinite abelian group

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Help showing this is an element of $(\mathbb{Z}/p^n\mathbb{Z})^{\times}$

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When $d \mid n$, the number of elements of order $d$ in a cyclic subgroup of order $n$ is $\phi (d)$

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Multivaritate version of Fermat's little theorem

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factorising polynomials related proofs

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Group of order $pq$ with $p<q$ prime has $q-1$ elements of order $q$

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Group $G$ cyclic as it coincides with the multiplicative group of a finite field

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Write $\mathbb{Z}^3/L$ as a direct sum of cyclic groups

Published on 19 Jul 2016 - 13:10

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Common generator of units in finite prime fields

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A group $G$ is locally cyclic if and only if $G$ is a union of a chain of cyclic subgroups ?

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List Question

Cyclic Field Extensions of sum of radicals

Proof check: Necessary and sufficient condition for $\langle x^r\rangle\subseteq\langle x^s\rangle$?

Confused about cyclic goups

Does my claim work for a set?

Let $G$ be a finite nilpotent group and $G'$ its commutator subgroup. Show that if $G/G'$ is cyclic then $G$ is cyclic.

A question on infinite abelian group

Help showing this is an element of $(\mathbb{Z}/p^n\mathbb{Z})^{\times}$

When $d \mid n$, the number of elements of order $d$ in a cyclic subgroup of order $n$ is $\phi (d)$

Multivaritate version of Fermat's little theorem

factorising polynomials related proofs

Group of order $pq$ with $p<q$ prime has $q-1$ elements of order $q$

Group $G$ cyclic as it coincides with the multiplicative group of a finite field

Write $\mathbb{Z}^3/L$ as a direct sum of cyclic groups

Common generator of units in finite prime fields

A group $G$ is locally cyclic if and only if $G$ is a union of a chain of cyclic subgroups ?

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