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May 7th, 2011, 05:18 AM  #1 
Newbie Joined: May 2011 Posts: 1 Thanks: 0  external direct product
How do you prove that the external direct product of any finite number of groups is a group?

May 7th, 2011, 08:43 AM  #2 
Senior Member Joined: Jun 2010 Posts: 618 Thanks: 0  Re: external direct product
Lila, The first thing is to define what the operation on the product is going to be. Of course, it is what you would expectcomponentwise addition (or multiplication, depending on what notation you are using). The second is to show that this operation makes the set (product) closed under the operation, etc., i.e. it satisfies all the group axioms. To that end, if and are written as so that the operation is defined by then you need to show that Ormkärr 

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