Given that G is a finite group, M is a finitely generated right free G-module and A is a left G-module, there exists a natural G-isomorphism $\phi\ : M\otimes_{\,G}A\rightarrow {Hom}_{G}({Hom}_{\,\mathbb Z}(M,{\,\mathbb Z}),A)$ given by $\phi\ (m\otimes_{}a):f↦f(m)a$ . I cannot prove that $\phi\ $is surjective. Would anyone please help me deal with this? I appreciate any help.
2026-03-28 22:37:57.1774737477
How to prove $M\otimes_{\,G}A≅ {Hom}_{G}({Hom}_{\,\mathbb Z}(M,{\,\mathbb Z}),A)$?
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