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\title{Math 420-620\\Fall 2012\\Homework 9}
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\centerline{\it Due Wednesday October 31, 2012.}

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\noindent 1. (5 pt) Let $p$ be a prime integer. Show that any group of order $p^2$ is abelian.

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\noindent 2. (5 pt) Find the smallest \textit{odd} integer such that there is a nonabelian group of order $n$. 


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\noindent 3. (5 pt) Classify all groups of order $n$ where $n$ is the answer from number 2.

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\noindent 4. (5 pt) Classify all abelian groups of order 64.

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\noindent 5. (5 pt) Let $G$ and $H$ be groups. Show that $Z(G\times H)=Z(G)\times Z(H)$


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