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.
Contact Us