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Homomorphism of a Group and Kernel of the Homomorphism

Modern Algebra
Group Theory (LIV)
Homomorphism of a Group
Kernel of the Homomorphism

Verify if the mapping defined is a homomorphism and in that case in which it is homomorphism, determine the Kernel:

G is any abelian group and ¯G = G, phi(x) = x^5 all x belongs to G.

The fully formatted problem is in the attached file.


Solution Summary

Homorphisms and kernels are investigated. The solution is detailed and well presented.