Let S be any set. A group G together with a fixed function g : S

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Let S be any set. A group G together with a fixed function g : S → G constitutes a blop group on S if for each group G' and map f : S → G' there exists a unique homomorphism ∅f of G into G' such that f = ∅g (see Fig. 39.15). 

a. Let S be a fixed set. Show that if both G1, together with g1 : S → G1, and G2, together with g: S → G2, are blop groups on S, then G1 and G2 are isomorphic. 

b. Let S be a set. Show that a blop group on Sexists. You may use any theorems of the text. 

c. What concept that we have introduced before corresponds to this idea of a blop group on S?


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