Characterize a free abelian group by properties in a fashion similar to that used in Exercise 13.
Question:
Characterize a free abelian group by properties in a fashion similar to that used in Exercise 13.
Data from Exercise 13
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 = ∅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 g2 : 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?
39.15 Figure
S 8 09 f G Pf G
Step by Step Answer:
The characterization is just like that in Exercise 13 with the requirement that both G and G be abelian groups Data from Exercise 13 a Consider the blop group G 1 on S and let G be the free group FS w...View the full answer
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