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Given two groups A$A$ and B$B$ and an injective homomorphism f: A → B$f : A \to B$. When does a homomorphism g: B → A$g : B \to A$ exist with gf = idA$g\circ f = \mathrm{id}_A$ (but not necessarily fg = idB$f\circ g = \mathrm{id}_B$)?
Given two groups A and B and an injective homomorphism f: A → B. When does a homomorphism g: B → A exist with gf = idA (but not necessarily fg = idB)?
Given two groups $A$ and $B$ and an injective homomorphism $f : A \to B$. When does a homomorphism $g : B \to A$ exist with $g\circ f = \mathrm{id}_A$ (but not necessarily $f\circ g = \mathrm{id}_B$)?
