\part{Symmetric Groups}

\chapter{Symmetric Group}
- permutation function
- symmetric group 
- Sym(n)	Symmetric group of order n
- matrix notation
- permutation group
\chapter{Cycles}
- cycle notation
- k-cycle
- transpostion (2-cycle)
- simple transpostion
\chapter{Properties of Cycles}
- disjoint cycles
- commutativity of disjoint cycles
- all bijections have unique disjoint cycle product representation
- cycle type
- conjugate cycle lemma
- cycle type-conjugation theorem
- inversion set
- properites of inversion set cardinality
- permutation signature
- signature homomorphism
- alternating group
- Alt(n)	Alternating group
- simple group
- Cayley's theorem

