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January 23rd, 2013, 09:28 AM   #1
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Normal Sub-group

If H is a subgroup of G such that x^2H for all xG ,then prove that H is a normal subgroup of G
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January 23rd, 2013, 10:36 AM   #2
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Re: Normal Sub-group

Quote:
Originally Posted by Taladhis
If H is a subgroup of G such that x^2H for all xG ,then prove that H is a normal subgroup of G
Taladhis, your five posts this morning give the appearance of someone posting their abstract algebra homework. If so, it would be considered appropriate for you to say what you've done and where you've gotten stuck.

If I'm misreading this, my apologies.
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January 23rd, 2013, 06:39 PM   #3
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Re: Normal Sub-group

bt plz inform me the proof.
yes i want the proof for my hometask.inform plz
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January 23rd, 2013, 11:41 PM   #4
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Re: Normal Sub-group

hint:

show that for any g in G, and h in H, that:

ghg and (g^-1)^2 are in H.

to prove the former, you may want to consider ghgh, first.
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January 27th, 2013, 04:50 AM   #5
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Re: Normal Sub-group

sir what is "ghgh"?
Inform clearly.please
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January 27th, 2013, 10:10 AM   #6
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Re: Normal Sub-group

ghgh is (g*h)*(g*h), the square of the product g*h in G.
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