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\title{Second Sylow Theorem}

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\begin{frame}\frametitle{Strategy (Second Sylow Theorem)}

\bt If $P$ and $K$ are Sylow $p$-subgroups of a group $G$, then there exists $x\in G$ such that $P=x^{-1}Kx.$
\et

\be
\visible<2->{\item<beamer:check@6-> The conjugates of $K$ are $K=K_1, \ldots, K_t,$ with $(p,t)=1$ (using Theorem 9.25).}
\visible<3->{\item<beamer:check@7-> The $P$-conjugates of the $K_i$ are other $K_i$ and partition $S=\{K_1, \ldots, K_t\}$ into sets of size $p^k$ (using Theorem 9.25).}
\visible<4->{\item<beamer:check@8-> One of the sets $K_i$ must have size $t_0.$}
\visible<5->{\item<beamer:check@9-> Lemma 9.26 implies $P=K_i.$}
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\ee



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