Permutation/Sign/Group homomorphism/Fact
< Permutation < Sign < Group homomorphism
The
sign mapping
S
n
⟶
{
1
,
−
1
}
,
π
⟼
sgn
(
π
)
,
{\displaystyle S_{n}\longrightarrow \{1,-1\},\pi \longmapsto \operatorname {sgn} (\pi ),}
is a
group homomorphism
.
Proof
,
Write another proof