Explore BrainMass
Share

Explore BrainMass

    Cyclic Groups, Generators and Orders of Elements

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    (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.

    © BrainMass Inc. brainmass.com October 9, 2019, 4:54 pm ad1c9bdddf
    https://brainmass.com/math/group-theory/cyclic-groups-generators-orders-elements-43681

    Attachments

    Solution Summary

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

    $2.19