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Is direct product of subgroups a subgroup?

  1. Jun 24, 2010 #1

    In the second paragraph of the following paper, there is a statement: "Because the direct product of subgroups is automatically a subgroup.."

    http://jmp.aip.org/jmapaq/v23/i10/p1747_s1?bypassSSO=1 [Broken]

    I don't see how that can be true...you can always take direct product of a subgroup with itself many times and create a group of order larger than the parent group...
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 24, 2010 #2


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    If H_1 is a subgroup of G_1 and H_2 is a subgroup of G_2 then H_1 x H_2 is a subgroup of G_1 x G_2. In particular, if H1 and H2 are subgroups of a group G, then H1 x H2 is a subgroup of G x G (you are right, not of G itself).

    I haven't read the article, but the authors might have meant this.
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