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    Cyclic Groups, Generators and Orders of Elements

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    (1) Let G be a group such that
    Show that G cannot be cyclic.

    (2) Show that a cyclic group with one generator has at most 2 elements.

    (3) Let a 2 G be an element of order two, and b 2 G an element of order three. Show that HK where H = (a) and K = (b) has order 6.

    See the attached file.

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    Solution Summary

    Cyclic groups, generators and orders of elements are investigated. The solution is detailed and well presented.