# Group Theory

Hello.

I was wondering how I could prove if a set of numbers along with some arbitrary operation is an abelian group.

## Answers and Replies

Don't you have a list of axioms which says "G is an abelian group if and only if the following are satisfied: ..."?

JasonRox
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The first step is proving that it is a group in the first place.

If it's not a group, than it certainly isn't an abelian group.

Then after that, look at the definition of what it means for a group to be abelian. Test it. Then you are done.

Hint: a*b = b*a (where * is the binary operation)

Sometimes it feels like people just repeat what I write.

JasonRox
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Muzza said:
Sometimes it feels like people just repeat what I write.

You said...

Don't you have a list of axioms which says "G is an abelian group if and only if the following are satisfied: ..."?

That's assuming that it is a group, but he hasn't even shown that yet. I'd worry about proving that it is a group before even thinking about what properties the group might have.

That's assuming that it is a group,

No it isn't. I even used the plural of "axiom" to try to hint at the fact that several things, rather than just commutativity, needed to be checked.

JasonRox
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Gold Member
Muzza said:
No it isn't. I even used the plural of "axiom" to try to hint at the fact that several things, rather than just commutativity, needed to be checked.

Good hint.