List questions from cyclic-groups

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List Question

$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.

What is $\frac{p\mathbb Z}{p^\alpha\mathbb Z}$?

Virtually cyclic groups are finitely generated

Necessary and sufficient condition for one cyclic group to be the subset of some other cyclic group.

Formal definition of cyclic order

Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group

Help explaining the sign of a permutation

Why are $321,213,132$ in cyclic order

Let $G$ be a group with $|G|=455$. Show that $G$ is a cyclic group.

Prove that G is cyclic if normal subgroup is of order 2

$G$ finite group, $H \trianglelefteq G$, $\vert H \vert = p$ prime, show $G = HC_G(a)$ $a \in H$

Prove that there are no simple groups of order 224.

A problem involving centralizer and cycles

Two equal cyclic subgroups of $S_n$ have conjugate generators

Generators of a finite additive cyclic group

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