
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 3  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: 3  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: 14,201 Thanks: 485 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


Tags 
abelian, abnanbn, group, show 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Abelian group  need help  hshimoni  Abstract Algebra  1  August 31st, 2013 09:15 PM 
Show group with order 595 is abelian.  watson  Abstract Algebra  4  December 20th, 2011 01:18 PM 
A torsion free abelian group G having a free abelian subgrou  johnmath  Abstract Algebra  9  April 25th, 2011 10:58 AM 
abelian group  santustus6  Abstract Algebra  1  November 12th, 2010 12:24 PM 
Is maxfunction an Abelian Group?  MageKnight  Algebra  3  January 1st, 1970 12:00 AM 