Give the solution to isomorphism

Reference no: EM13124005

The solution to Isomorphism

Let H be a group and tau_1 : H ---->G_1, tau_2 : H ----> G_2, ... , tau_n : H -----> G_n homomorphism with this property: whenever G is a group and g_1 : G ---->G_1, g_2 : G ----G_2, ..., g_n : G ----> G_n are homomorphism, then there exists a unique homomorphism g* : G ----> H such that (tau)_i â?¢ g* = g_i for every i. Prove that H is isomorphic to G_1 x G_2 x ... x G_n.

Reference no: EM13124005

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