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January 21st, 2014, 09:14 AM   #1
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direct product

How can I prove that direct product of two groups is group? Or it did not?
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January 21st, 2014, 11:52 AM   #2
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Re: direct product

Depending on how you define the binary operator.
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January 22nd, 2014, 10:20 AM   #3
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Re: direct product

I need to determine a direct prodcut binary operation that operate and if is possible direct product that doesn't operate or vice versa.
Tell me - I don't know how to do it.
May one look on it and tell me how to deal with it.
Thanks, for the responders.
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January 22nd, 2014, 10:47 AM   #4
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Re: direct product

If you are given two groups with binary operations (G, g) and (H, h) use the binary operator over G x H as (g, h). You have a group then.
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January 22nd, 2014, 12:05 PM   #5
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Re: direct product

I don't understand which opeartion you decide to use? What is the operation you choose? I think you choose operation of Cartesain product? But what is the result? (I think it's a point).
Please someone expand and explain the operation that operate here.
Thanks and Bless you.
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January 22nd, 2014, 05:30 PM   #6
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Re: direct product

Quote:
Originally Posted by shaharhada
I don't understand which opeartion you decide to use? What is the operation you choose? I think you choose operation of Cartesain product? But what is the result? (I think it's a point).
Please someone expand and explain the operation that operate here.
Thanks and Bless you.
Each of G and H are groups. So you combine pairs (g, h) and (g', h1') using the respective group operations on G and H. In other words

(g, h) * (g', h1') = (gg', hh')

where gg' is defined by the group operation on G; and hh' is defined by the group operation on H.
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January 23rd, 2014, 10:28 AM   #7
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More question:

I have a more question:
What is the identity element of the operating group result?
Thanks for the guys who help me.
How I find the identity element?
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January 23rd, 2014, 06:34 PM   #8
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Re: direct product

The identity of GxH is the pair:

where each of these is the identity element in their respective groups.
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