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## Homework Statement

I want to find the kernel of PHI: Z-> Z (mod 24) X Z (mod 81)

I am beginning to think that the kernel of this is actually just the set containing the identity element, or the trivial subgroup of Z mod 24. I am thinking this because none of the subgroups of Z mod 24 are equal to the identity of Z mod 81. Am I thinking about this correctly??

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