# Dawid Kielak's homepage

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## Congruence Subgroup Property

1. $\mathrm{SL}_n(\mathbb{Z})$: We looked at the proof of the CSP, as given by Mennicke, building on the work of Brenner.
2. $\mathrm{Out}(F_n)$: We start by looking at the paper of Stallings to show that $\mathrm{Aut}(F_n)$ is finitely generated. To give a presentation we prove the peak reduction lemma as given by Higgins--Lyndon , then look at the paper of McCool, and conclude with the paper of Gersten.