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#1 2009-06-08 17:39:04
- matt00hew
- Novice
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Group of order 512
I'm interested in a problem that has turned out to be a group of order 512. Abelian and non cyclic. Is there a catalogue somewhere so I can find out which group it is? Or tests to do to narrow down the options?
#2 2009-06-09 00:12:51
- JaneFairfax
- Legendary Member
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Re: Group of order 512
If you want Abelian, that’s easy. Any non-cyclic Abelian group is isomorphic to one of the following:
The result you need is the fundamental theorem of finite Abelian groups.
#3 2009-06-09 00:49:51
- mathsyperson
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Re: Group of order 512
Also
Why did the vector cross the road?
It wanted to be normal.
#4 2009-06-09 04:59:56
- Ricky
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Re: Group of order 512
This is where
is the integers modulo n. Jane, why the notation with C? I typically see this in applications to physics and chemistry, but normally the group theoretic:
Or the number theoretic:
notations are used by mathematicians. Just curious where you got it from.
"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..."
#5 2009-06-09 21:34:59
- matt00hew
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Re: Group of order 512
Thank you! That's incredibly helpful. Now I've seen your list it all makes sense.
#6 2009-06-10 05:09:21
- JaneFairfax
- Legendary Member
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Re: Group of order 512
No, no. is not . It’s the cyclic group of order . This notation is used by Humphreys.
#7 2009-06-10 08:23:01
- Ricky
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Re: Group of order 512
Jane,
is the cyclic group of order n."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..."