(a) Let G and G′ be finite groups whose orders have no common factors. Show that...

(a) Let G and G′ be finite groups whose orders have no common factors. Show that the only homomorphism φ:G→G′ is the trivial one.

(b) Give an example of a nontrivial homomorphism φ for the given groups, if an example exists. If no such homomorphism exists, explain why.

i.φ: Z16→Z7

ii.φ: S4→S5

Expert Solution

Colby Messinger answered 1 year ago

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