Exercise
For n at least 3, the identity element in Sn can be written as a product of an odd number of
3-cycles
2-cycles
4-cycles
Yes, (1,2,3)(1,2,3)(1,2,3) = e.
No, because the identity can also be written as (1,2)(1,2), an even
number of transpositions.
No, because such a product is also a product of an odd number of 2-cycles.