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#1 2007-11-12 06:06:18

dchilow
Member
Registered: 2007-03-05
Posts: 27

Need Help with abstract algebra!

Let G be a group and assume that every nonidentity element of G has order two.  Prove that G is abelian.

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#2 2007-11-12 06:37:32

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Need Help with abstract algebra!

Well, if you take a,bG

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#3 2007-11-12 11:48:41

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Need Help with abstract algebra!

Alternate proof:

a^2 = 1, so a = a^-1.  Hence, ab = a^-1b^-1 = (ba)^-1 = ba.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#4 2007-11-12 11:57:05

dchilow
Member
Registered: 2007-03-05
Posts: 27

Re: Need Help with abstract algebra!

Thank you JaneFairfax.  You were a great help!

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#5 2007-11-12 11:59:31

dchilow
Member
Registered: 2007-03-05
Posts: 27

Re: Need Help with abstract algebra!

That is another good one, Ricky.  Thanks.

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