01-31-2005, 11:21 AM
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#1 (permalink) |
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Will power
 
Join Date: Nov 2002
Location: Hanoi and Munich
Posts: 401
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Abelian group
A group G in which (a*b)^2 = a^2 * b^2 for all a, b in G is necessarily
(A) finite (B) cyclic (C) of order two (D) abelian (E) none of the above Answer key: SPOILER: D The answer key says this is an Abelian group. How would you prove the commutativity? Thanks, vvaann
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01-31-2005, 11:31 AM
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#2 (permalink) |
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Within my grasp!
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Join Date: Nov 2004
Posts: 101
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Re: Abelian group
Oh, I love these...
 Don't forget: modern algebra (in ETS tests) is about shifting, shuffling and tossing letters to and fro.  What we know is: (ab)(ab) = (aa)(bb) Since the group operator is associative (we apply this on both sides) we have: a(ba)b = a(ab)b Now multiply both sides by inv(b) from the right and also by inv(a) from the left, and there it is... Md. |
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01-31-2005, 08:12 PM
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#3 (permalink) |
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Will power
Join Date: Nov 2002
Location: Hanoi and Munich
Posts: 401
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Re: Abelian group
Very nice!
Thanks again, matroid! It's lucky to have a chance to practice math with you Br, vvaann
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Go to TWE section and learn writing with me. Correct my essays and I will participate in reviewing yours! |
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