Is direct product of subgroups a subgroup?

  • #1

Main Question or Discussion Point

Hi..

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...
 
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Answers and Replies

  • #2
Landau
Science Advisor
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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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