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February 3rd, 2011, 12:34 PM  #1 
Joined: Feb 2011 Posts: 13 Thanks: 0  Show that (ab)^n=(a^n)(b^n) for an Abelian group
I'm having problem with this proof: Let a and be be elements of an Abelian group and let ne be any integer. Show that (ab)^n=(a^n)(b^n). Is this true for non Ablelain groups. I am two weeks in to my course in Abstract Algebra and I have an exam need week. Really nned help because I am gettine myself so confused!

February 3rd, 2011, 01:22 PM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Show that (ab)^n=(a^n)(b^n) for an Abelian group
Well, what is (ab)^n ?? It's just (ab)(ab)(ab)(ab).........(ab) n times. But since you're talking abelian, you can move the elements around, so you can write (aaaaaaaaaaaaaaaa.........a)(bbbbbbbbbbbbbbbbbb... .....b) Where each of a and b is written n times, but that's just (a^n)(b^n) This is not true in nonabelian groups. 
February 3rd, 2011, 02:53 PM  #3 
Joined: Feb 2011 Posts: 13 Thanks: 0  Re: Show that (ab)^n=(a^n)(b^n) for an Abelian group
Thats bascially what i had only i thought it was too simple!! Thanksvery much! 
February 3rd, 2011, 02:55 PM  #4 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Show that (ab)^n=(a^n)(b^n) for an Abelian group
You can also (repeatedly) multiply by a^1 on the left and b^1 on the right....

February 3rd, 2011, 03:23 PM  #5 
Joined: Feb 2011 Posts: 13 Thanks: 0  Re: Show that (ab)^n=(a^n)(b^n) for an Abelian group
But the first option is still ok for a proof right??

February 3rd, 2011, 03:40 PM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 15,389 Thanks: 770 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic  Re: Show that (ab)^n=(a^n)(b^n) for an Abelian group Quote:
 
February 5th, 2011, 04:23 AM  #7 
Joined: Feb 2011 Posts: 13 Thanks: 0  Re: Show that (ab)^n=(a^n)(b^n) for an Abelian group
Ok thanks Ill try that


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abelian, abnanbn, group, show 
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