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    Proofs in Group Theory : Cayley Table, Subsets and Cosets - Five Problems

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    Five Problems:

    Let G=[FORMULA1], with operation given by multiplication modulo 14.

    1) by computing the Cayley table of G, or otherwise, show the G is a group. You may assume that without proof multiplication modulo 14 is associative.
    2) Prove that the subset H={1,9,11} is a subgroup of G
    3) Compute the left cosets of G and H ...

    (Please see attachment for proper citation of formulas and for problems 4 and 5).

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    Solution Summary

    Cayley Table, subsets and cosets are investigated. The solution is well presented.