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    Direct product

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    Let G1 and G2 be groups, and let G be a direct product of G1 x G2.
    Let H = {(x1, x2) element G1 x G2 | x2 = e} and let K = {(x1, x2) element G1 x G2| x1 = e}.

    (a) Show that H and K are subgroups of G.
    (b) Show that HK = KH = G
    (c) Show that H [see attachment] K = {(e,e)}.

    © BrainMass Inc. brainmass.com October 9, 2019, 4:22 pm ad1c9bdddf
    https://brainmass.com/math/group-theory/direct-product-groups-30330

    Attachments

    Solution Preview

    Please see the attachment.

    Proof:
    , are groups, . Let be the identity of group and be identity of group . Then , .
    (a) Show that and are subgroups of ...

    Solution Summary

    This is a proof regarding subgroups.

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