Order of Permutation Group

Order of Permutation-: For a given permutation P if  Pⁿ= I (identity permutation) , then n is the order of permutation.

Let a permutation 

and  Pⁿ = I =

Then n is the order of permutation.

Example 1-:  How many times be multiplied to itself to produce 

Solution-: Let      P=

   Then P²=P.P=

                             P²=

                             P³= P².P=

                             P³==I

Hence the required number is 3.

Order=3

Example 2-: Find the order of permutation .

Solution-:  Let the given permutation be P= 

                   We can write P as P= 

                  P²=

                      =

                 P³=P².P=

                             =

                 P⁴=P³.P=

                              =

P⁴=I (identity permutation)

Hence, order is 4.