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    Cosets of Subgroups of a Group

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    Modern Algebra
    Group Theory (XXVII)
    Subgroups of a Group
    Cosets of Subgroups of a Group

    For a subgroup H of G define a left coset of H in G as the set of all elements of the form ah, h in H.
    Show that there is a 1-1 correspondence between the set of left cosets of H in G and the set of right cosets of H in G.

    The fully formatted problem is in the attached file.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:47 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/cosets-of-subgroups-of-a-group-62307

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    Solution Summary

    It shows that there is a 1-1 correspondence between the set of left cosets of H in G and the set of right cosets of H in G.
    The solution is detailed and well presented.

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