## A difficult exercise

While proctoring the make-up exam for my class, I thought of an exercise related to my group theory posts on direct and free products that should cause even the more experienced mathematicians in the audience a bit of difficulty.

Consider four groups , , , and , and four homomorphisms:

Use these to construct two homomorphisms from to , and show that they’re the same.

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Is it time for a hint? 😉

Where to find the second homomorphism?

Comment by edriv | December 11, 2007 |

One comes from each universal property. One from the product and one from the coproduct.

Comment by John Armstrong | December 11, 2007 |