Let G and H be groups, and suppose φ : G → H is operation-preserving (that is, φ(ab) = φ(a)φ(b) for all a, b ∈ G). Let e
Posted: Wed May 11, 2022 11:13 pm
Let G and H be groups, and suppose φ : G → H is
operation-preserving (that is, φ(ab) = φ(a)φ(b) for all a, b ∈
G).
Let e_G and e_H be the identities of G and H,
respectively. Show that φ(e_G) = e_H.
operation-preserving (that is, φ(ab) = φ(a)φ(b) for all a, b ∈
G).
Let e_G and e_H be the identities of G and H,
respectively. Show that φ(e_G) = e_H.