Suppose that G is a group with subgroups K ≤ H ≤ G . Suppose that K is normal in G . Let G act on G / H , the set of left cosets of H , by left multiplication. Prove that if k ∈ K , then left...

Suppose that
G
is a group with subgroups
K
≤
H
≤
G. Suppose that
K
is normal in
G. Let
G
act on
G/H, the set of left cosets of
H, by left multiplication. Prove that if k ∈
K, then left multiplication of
G/H
by k is the identity permutation on
G/H.