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## #1 2009-06-07 19:39:04

matt00hew
Member
Registered: 2009-06-07
Posts: 2

### 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?

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## #2 2009-06-08 02:12:51

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

### 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.

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## #3 2009-06-08 02:49:51

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Group of order 512

Also

Why did the vector cross the road?
It wanted to be normal.

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## #4 2009-06-08 06:59:56

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

### 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..."

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## #5 2009-06-08 23:34:59

matt00hew
Member
Registered: 2009-06-07
Posts: 2

### Re: Group of order 512

Thank you! That's incredibly helpful. Now I've seen your list it all makes sense.

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## #6 2009-06-09 07:09:21

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

### Re: Group of order 512

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

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## #7 2009-06-09 10:23:01

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

### 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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