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 φ
Posted: Wed May 11, 2022 11:14 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 φ(G) = {φ(g)|g ∈ G}. Assume that φ is one-to-one. Show
that φ is an isomorphism if and only if φ(G) = H.
operation-preserving (that is, φ(ab) = φ(a)φ(b) for all a, b ∈
G).
Let φ(G) = {φ(g)|g ∈ G}. Assume that φ is one-to-one. Show
that φ is an isomorphism if and only if φ(G) = H.