Homomorphism proof

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Homework Statement


If f:G[tex]\rightarrow[/tex]H is a homomorphism, then f(eG) = eH.


Homework Equations


The proof from my professor's notes:
f(eG) = f(eG*GeG) = f(eG)*f(eG)
f(eG) = f(eG)*eH
f(eG)*f(eG) = f(eG)*eH
f(eG) = eH

The Attempt at a Solution

My question is, how do you get from the first line to the second. Because it looks like she's using the proposition to prove itself.
 

Answers and Replies

  • #2
Petek
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The second line doesn't follow from the first. It simply says that if you multiply any element of H by the identity element of H, you get ... (fill in the rest).

Petek
 
  • #3
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The second line doesn't follow from the first. It simply says that if you multiply any element of H by the identity element of H, you get ... (fill in the rest).

Petek
:blushing: I feel like an idiot. Thank you!
 

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