Abstract Algebra/Group Theory/Homomorphism/Homomorphism Maps Identity to Identity

< Abstract Algebra‎ | Group Theory‎ | Homomorphism

TheoremEdit

Let f be a homomorphism from group G to group K.

Let eG and eK be identities of G and K.

f(eG) = eK

ProofEdit

0.   f maps to K
1.   inverse in K
.
2.   f is a homomorphism
3.   identity eG
.
4.   1.
.
5.   identity eK, definition of inverse
6.   identity eK