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    Problems in Group Theory

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    Let G_1 and G_2 be groups and ?:G_1?G_2 a map. Which of the following is a group homomorphism? Explain your answers. If ? is a homomorphism, describe the kernel and the image of ?.

    a) G_1=C_4=?a|a^4=e?,G_2=Z_2 (the integers modulo 2 with the operation +), ?:a^i?i (mod 2).

    b) G_1=G_2=Z_5 (the integers modulo 5 with the operation +), ?:n?an(mod5) where a?Z_5{0}={1,2,3,4} is fixed.

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    https://brainmass.com/math/group-theory/problems-group-theory-homomorphism-455433

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    Let (please see the attached file) and (please see the attached file) be groups and (please see the attached file) a map. Which of the following is a group ...

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    In this solution, we solve various problems in group theory.

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