The cyclic group of order 2020

#group_theory

Let $G$ be the additive group $Z_{2020}$ and let $H \subseteq G$ be the subset consisting of those elements with order dividing 20.

Prove $H$ is a subgroup of $G$ .
Find an explicit generator for $H$ and determine its order.

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L A T E X

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Let $G$ be the additive group ${\bf Z}_{2020}$ and let $H\subseteq G$ be the subset consisting of those elements with order dividing 20.
\begin{enumerate}[label=\alph*)]
	\item Prove $H$ is a subgroup of $G$.
	\item Find an explicit generator for $H$ and determine its order.
\end{enumerate}