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    Homomorphism of a Group and Kernel of the Homomorphism

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    Modern Algebra
    Group Theory (L)
    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 the group of non-zero real numbers under multiplication, ¯G = G, phi(x) = x^2 all x belongs to G.

    The fully formatted problem is in the attached file.

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    Solution Summary

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