====== Examples Of Abstract Groups ======
==== Problem ====
Give examples of [[definition:group|groups]] with the following properties. Feel free to make them as simple as possible.
  - A finite [[definition:abelian group]]
  - A finite [[definition:abelian group|nonabelian group]]
  - A finite [[definition:group]] with exactly one  proper nontrivial [[definition:subgroup]]
  - An infinite [[definition:abelian group]]
  - An infinite [[definition:abelian group|nonabelian group]]
  - An infinite [[definition:group]] in which no nontrivial element has finite [[definition:Order (for groups)|order]]
  - An infinite [[definition:group]] in which every element has finite [[definition:Order for groups|order]]
  - An infinite [[definition:group]] with exactly one nontrivial element of finite [[definition:Order for groups|order]]

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==== Remarks ====  
  * None.

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==== $\LaTeX$ version ====
<file tex problem.examples_of_abstract_groups.tex>
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\begin{problem}
Give examples of groups with the following properties. Feel free to make them as simple as possible.
\begin{enumerate}
\item A finite abelian group
\item A finite nonabelian group
\item A finite group with exactly one  proper nontrivial subgroup
\item An infinite abelian group
\item An infinite nonabelian group
\item An infinite group in which no nontrivial element has finite order
\item An infinite group in which every element has finite order
\item An infinite group with exactly one nontrivial element of finite order
\end{enumerate}
\end{problem}
</file>

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==== External links ====
  * None.

{{tag>problem needsreview rjosh}}