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#1 2009-06-08 17:39:04

matt00hew
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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
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Re: Group of order 512

If you want Abelian, thats 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. smile


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#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
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Re: Group of order 512


No, no.
is not
. Its the cyclic group of order
. This notation is used by Humphreys.


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#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..."
 

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