Need help with 531 i SolutionSolution 531 i Proof Let A B

Need help with 5.31 i

Solution

Solution : 5.31 ( i )

Proof.

Let A, B, C be groups, : A B, : B C be group morphisms, and x, y A. It follows that

[ ](xy) = ((xy)) = ((x)(y)) = ((x))((y)) = [ ](x) · [ ](y),

so the composition is a homomorphism of groups.