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# Group Theory Problem watch

1. I cannot understand how to get started on this problem:

Let T ={0,1,2}

How many different binary operations * can you define on T?

For how many of these is (T,*) a group.

I think there will be 9 operations but the secon part of the question is beyond me

Can anyone help?
2. There are a lot more than 9 possible binary operations.

(Hint: How many possible values are there for 0 * 0? For 0 * 1? For 0 * 2? For 1 * 0? ...).

For the 2nd part: You have 3 choices for the identity; once you know the identity it's easy to list the possible group tables.

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Updated: April 3, 2011
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