Is mapping generators to generators, and then extending, a well-defined homomorphism?Is the bijection shown by commutativity?About a well-defined homomorphismExample of non isomorphic groups with isomorphic group algebrasSubgroup of free products is torsion-freeSpecifying a homomorphism by given the images of the generators and extending “lineary”Definition of subgroup of abelian group $G$ generated by subset $A$Hatcher's definition of direct limit of a sequence of homomorphisms of abelian groupsLet $G,H$ be groups and $varphi:G times Hto G$ and $H'=ker(varphi)$. Show that $(Gtimes H)/H'cong G$Extending group homomorpisms by defining image of generators.
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