Compute the order of 1 2 35 6 in Sym6SolutionTo compute orde

Compute the order of (1, 2, 3)(5, 6) in Sym(6).

Solution

To compute order of disjoint cycles we have formuls

count element in each disjoint cycles namely as a,b,c,d.......

order of disjoint cycles = Lcm(a,b,c,d,.....)

here disjoint cycles are (1,2,3)(5,6)=Lcm(3,2)

=6

order is 6