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\title{Groups of order 8}

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\begin{frame}\frametitle{Strategy (Groups of order 8)}

\bt If $G$ is a group of order 8, then $G\cong \Z_8, \Z_4\times \Z_2, \Z_2\times\Z_2\times \Z_2, D_4,$ or $Q$ (the quaternions).
\et

\be
\visible<2->{\item<beamer:check@6-> If $G$ is abelian, it is in the list.  Assume $G$ is not abelian.}
\visible<3->{\item<beamer:check@7-> $G$ must have an element $a$ of order $4.$ $<a>\trianglelefteq G.$}
\visible<4->{\item<beamer:check@8-> Let $b\in G-<a>.$ $G=\{e,a,a^2,a^3,b,ab,a^2b,a^3b\}.$}
\visible<5->{\item<beamer:check@9-> $ab\ne ba.$}
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\ee



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