Abstract Algebra: Theory and Applications · Problem 9.4.26

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · isomorphism-identity

Problem

Let

\phi : G \to H

be a group isomorphism. Show that

\phi(x) = e_H

if and only if

x = e_G

, where

e_G

and

e_H

are the identities of

G

and

H

, respectively.