Math Help - order of a permutation

1. order of a permutation

Find the order of g,

S7= Sym(7)=Symmetric group 7

G = S7, g = (1 3 5)(2 4 6 7).

My answer is ord(g) = 12

I know you suppose to find the lowest common multiple to find the order.. but what Im not sure about is:

If g was not disjoint
do you multiply together and then find its order or can you find the order the way its given.

2. Originally Posted by Dreamer78692
Find the order of g,

S7= Sym(7)=Symmetric group 7

G = S7, g = (1 3 5)(2 4 6 7).

My answer is ord(g) = 12

I know you suppose to find the lowest common multiple to find the order.. but what Im not sure about is:

If g was not disjoint
do you multiply together and then find its order or can you find the order the way its given.
Good question!

The answer, however, is no. Remember that the set of 2-cycles generates the group $S_n$, and so if it were true then every element would have order 2.

For example, (12)(23) = (132). lcm(2, 2)=2 but the order of (132) is 3. So there is your counter-example.