Rewrite symmetric groups

src/Advanced/Symmetric Groups/main.typ

@@ -0,0 +1,35 @@
+#import "@local/handout:0.1.0": *
+
+#show: handout.with(
+  title: [Symmetric Groups],
+  by: "Mark",
+)
+
+#include "parts/00 intro.typ"
+#pagebreak()
+
+#include "parts/01 cycle.typ"
+#pagebreak()
+
+#include "parts/02 groups.typ"
+#pagebreak()
+
+#include "parts/03 subgroup.typ"
+#pagebreak()
+
+= Bonus problems
+
+#problem()
+Show that $x in ZZ^+$ has a multiplicative inverse mod $n$ iff $gcd(x, n) = 1$
+
+#v(1fr)
+
+#problem()
+Let $sigma = (sigma_1 sigma_2 ... sigma_k)$ be a $k$-cycle in $S_n$, and let $tau$ be an arbitrary element of $S_n$. \
+Show that $tau sigma tau^(-1)$ = $(tau(sigma_1), tau(sigma_2), ..., tau(sigma_k))$ \
+#hint[$tau$ is a permutation, so $tau(x)$ is the value at position $x$ after applying $tau$.]
+
+#v(1fr)
+#problem()
+Show that the set ${ (1, 2), (1,2,...,n)}$ generates $S_n$.
+#v(1fr)