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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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# Is direct product of subgroups a subgroup?

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