January 23rd, 2013, 09:28 AM  #1 
Newbie Joined: Jan 2013 From: west bengal,india Posts: 22 Thanks: 0  Normal Subgroup
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  
Senior Member Joined: Aug 2012 Posts: 2,306 Thanks: 706  Re: Normal Subgroup Quote:
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 Subgroup
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 Subgroup
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 Subgroup
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 Subgroup
ghgh is (g*h)*(g*h), the square of the product g*h in G.


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