Tag: free-groups
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An explanation of Commutative Diagrams
Here is a short project I wrote which defines commutative diagrams in terms of directed graphs. I wrote this project because I couldn’t find a good source of information online which explained commutative diagrams to my satisfaction.
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Free groups generated by the same free set are isomorphic
Source: Geometric Group Theory: An Introduction, Clara Löh, but is a standard exercise. Problem: Let be a set. Then, up to isomorphism, there is at most one group freely generated by . Proof: Let and be groups with free generating set . Let and be the inclusion maps from into and respectively. By the universal…