Question

Which of the following statements are true/false?Give reasons for your answers. 1.If σ is an even permutation,then σ^2=1.

Answer 1

False

Explanation:

An even permutation can be decomposed into an even number of transpositions.

For example `((2, 3))` followed by `((1, 2))` is equivalent to `((1, 2, 3))`

So if `sigma = ((1, 2, 3))` then `sigma^3 = 1` but `sigma^2 = ((1, 3, 2)) != 1`