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Group homomorphism

Source: IMS 2014 - Day1 - Problem5

October 4, 2014
group theoryabstract algebrasuperior algebrasuperior algebra unsolved

Problem Statement

Let G1G_1 and G2G_2 be two finite groups such that for any finite group HH, the number of group homomorphisms from G1G_1 to HH is equal to the number of group homomorphisms from G2G_2 to HH. Prove that G1G_1 and G2G_2 are Isomorphic.
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