The sign of an even permutation is +1 and the sign of an odd permutation is -1. Observe th...

The sign of an even permutation is +1 and the sign of an odd permutation is -1. Observe that the map sgnn : Sn → {1, -1} defined by

is a homomorphism of Sn onto the multiplicative group {1. -1}. What is the kernel? Compare with Example 13.3.