Let G be any group. An abelian group G^* is a blip group of G if there exists a fixed homomorphism ∅ of G onto G^* such that each homomorphism ψ of G into an abelian group G' can be factored as ψ = θ∅, where θ is a homomorphism of G^* into G' (see Fig. 39.14). 

a. Show that any two blip groups of G are isomorphic.

b. Show for every group G that a blip group G* of G exists. 

c. What concept that we have introduced before corresponds to this idea of a blip group of G?

 

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@ 39.14 Figure G S 8 f 39.15 Figure Pf