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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
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- Registered: 2007-02-23
- Posts: 6,868
Re: Need Help with abstract algebra!
Well, if you take a,b ∈ G
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#3 2007-11-12 11:48:41
- Ricky
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- 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
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- 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
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- Registered: 2007-03-05
- Posts: 27
Re: Need Help with abstract algebra!
That is another good one, Ricky. Thanks.
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