Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

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

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?

Offline

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

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.

Offline

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

Also

Why did the vector cross the road?

It wanted to be normal.

Offline

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

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..."

Offline

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

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

Offline

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

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

Offline

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

Jane,

"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..."

Offline

Pages: **1**