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 January 23rd, 2013, 09:28 AM #1 Newbie   Joined: Jan 2013 From: west bengal,india Posts: 22 Thanks: 0 Normal Sub-group If H is a subgroup of G such that x^2€H for all x€G ,then prove that H is a normal subgroup of G
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^2€H for all x€G ,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.

 January 23rd, 2013, 06:39 PM #3 Newbie   Joined: Jan 2013 From: west bengal,india Posts: 22 Thanks: 0 Re: Normal Sub-group bt plz inform me the proof. yes i want the proof for my hometask.inform plz
 January 23rd, 2013, 11:41 PM #4 Senior Member   Joined: Mar 2012 Posts: 294 Thanks: 88 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.
 January 27th, 2013, 04:50 AM #5 Newbie   Joined: Jan 2013 Posts: 7 Thanks: 0 Re: Normal Sub-group sir what is "ghgh"? Inform clearly.please
 January 27th, 2013, 10:10 AM #6 Senior Member   Joined: Mar 2012 Posts: 294 Thanks: 88 Re: Normal Sub-group ghgh is (g*h)*(g*h), the square of the product g*h in G.

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