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Subgroup of direct product

  1. Apr 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Let G1, G2 be groups with subgroups H1,H2. Show that

    [{x1,x2) | x1 element of H1, x2 element of H2} is a subgroup of the direct product of G1 X G2

    3. The attempt at a solution
    I'm not sure how to begin solving this problem.
  2. jcsd
  3. Apr 27, 2008 #2


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    Homework Helper

    Show it the usual way you show a set is a subgroup. Show H1xH2 is closed under the group operation, that it has an identity, that it has inverses, etc.
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