Symmetric Group

All permutations on \(n\) objects i, denoted \(S_n\) or \(\text{Sym}(n)\) , forms the Symmetric Group.

A group with all permutations is not much interesting. Some ways to form groups that don't include all permutations:

1. Taking \(m

   Sym(3) < Sym(4)

2. We can take a few elements (called the generator of the group) then multiply (compose) them to satisfy the closure property

Backlinks

• Group Theory