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 February 3rd, 2011, 12:34 PM #1 Newbie   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 non-abelian groups.
 February 3rd, 2011, 02:53 PM #3 Newbie   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 Newbie   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
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Re: Show that (ab)^n=(a^n)(b^n) for an Abelian group

Quote:
 Originally Posted by Elladeas But the first option is still ok for a proof right??
It's still a proof. If you're expected to be more formal than that, use induction to show it works.

 February 5th, 2011, 04:23 AM #7 Newbie   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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if g is an abelian group prove that a b n a n b n

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