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Quick question about subgroups and external direct products

  1. Mar 8, 2010 #1
    If A and B are groups, then A x B is a group....does the same hold for subgroups? i.e. if A' is a subgroup of A and B' for B, then is A' x B' a subgroup of A x B?

    Cheers,
    W. =)
     
  2. jcsd
  3. Mar 8, 2010 #2
    Well, does it contain the identity? Is it closed under multiplication (componentwise)? Inverses?
     
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