I want to list the elements of

So from my understanding, with

But I'm having trouble trying to make senses of the two other conditions, and how to properly translate them into the table.

Thank you!!!

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- Sep 15th 2008, 07:41 AMtttcomraderQuestion about presentation of cyclic group
I want to list the elements of

So from my understanding, with

But I'm having trouble trying to make senses of the two other conditions, and how to properly translate them into the table.

Thank you!!! - Sep 15th 2008, 09:22 AMOpalg
Notice first that .

From the relation it follows that . Using that, in any product of a's and b's you can always push the a's to the left of the b's. For example . In that way, you can express any element of the group as , with and . That gives you 24 elements of the group, and you still have a fair amount of work to do if you want to write down the whole multiplication table. - Sep 15th 2008, 01:10 PMNonCommAlg
and to complete

**Opalg**'s argument (Smile): also note that since and every element of can be written as with and it's easy to show that this

presentation is unique. so is a group of order with elements the group is called dicyclic group.