Sign homomorphism (from the symmetric group)
The sign homomorphism is given by sending a permutation \(\sigma\) in the symmetric group \(S_n\) to \(0\) if we can make \(\sigma\) by multiplying together an even number of transpositions, and to \(1\) otherwise.
The sign homomorphism is well-defined.
- Symmetric group
The symmetric groups form the fundamental link between group theory and the notion of symmetry.