Central homomorphism

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Definition

Suppose G_1 and G_2 are groups. A homomorphism of groups \varphi:G_1 \to G_2 is termed a central homomorphism if it satisfies the condition that \varphi(Z(G_1)) \le Z(G_2), where Z(G_1) and Z(G_2) denote respectively the centers of G_1 and G_2 respectively.

Facts