The sign homomorphism is given by sending a permutation in the Symmetric group to if we can make by multiplying together an even number of transpositions, and to otherwise.
%%%knows-requisite(Modular arithmetic): Equivalently, it is given by sending to the number of transpositions making it up, modulo . %%%
The sign homomorphism is well-defined.
%%%knows-requisite(Quotient group): The Alternating group is obtained by taking the quotient of the symmetric group by the sign homomorphism. %%%